![](data:image/gif;base64,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)
А отсюда легко следует утверждение теоремы.
Замечание. Можно показать, что если в правой части уравнения вместо функции
![](data:image/gif;base64,R0lGODlhHAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAXAA8AhQAAAAAAAB4AHh0AHQEAAAAAAQAAHQAAHgAAMx0AMx0AMgAAMgEAMgAdSAAdRwAA/wAzWgAzWx1Ibh1GbB1IajIAHTIAATMAADMAHTMAMzVIbjNdgDNbgEgdAUYcAFUAAEgcAEcdAEgeNFozAFkzAl1/f1V3d0Rqe1V3f0huf113d1VublV3akhzgG5IHWxGHX9ZM25bNXd3VX9/XX93VXtqRGZmVXd3XX9uSHd3ZmaIiIBbM4BdM4BzSIiIZqoAAAZsQIBwSCwaj8ZMElmEIZAC5lDJTEgBkmJtcBpCiJ0AYQKoFEeEQmCoGFoogBcg9jwXL0JPREiC14lmRBdkBkIXXy9/Qw13cWoLRIoAIEZ4AAxDUVdsQiEBAQ5DI0UBB0QvX0wYm1ealRusVExBADs=)
поставить функцию
![](data:image/gif;base64,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)
которая либо ограничена для всех
![](data:image/gif;base64,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)
, либо для
![](data:image/gif;base64,R0lGODlhIQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAdAAwAhQAAAAAAAB0AHQEAAAAAAR0AAB4AAAAAHgAAMwAAMh0AMgAcSAAdSQAAVQAdSAAdRwEdSAAAqgAA/wAzWwAzWh1GbB1Ibh1IajMAADIAHTFZfTNZfzVIbjNbgDNdgEgcAEgdAEgeNFozAF1/f0Rqe1VmZkhuf113d1V3akhzgGpGHWpIHWxGHX9ZM39/XXtqRH9uSHd3VXd3XW5uVWaIiIBbM4BdM4iIZqoAAP8AAAECAwECAwECAwECAwECAwECAwZiQIBwSCwaj8jkURUIKJ9FhBBTfB2dys5wQRQkA4yjdzgWDQgBT7KQINakQ6pQBMVgh/CpVmhKGtpFb0QFQw5IAQ9JY0JjH0crUAAbhUIKACGRRhBTQwEHKUUrTaNNFKFNQ0EAOw==)
существует непрерывная функция
![](data:image/gif;base64,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)
такая, что при всех
![](data:image/gif;base64,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)
выполняется неравенство
![](data:image/gif;base64,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)
, то все решения уравнения
![](data:image/gif;base64,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)
при тех же предположениях относительно функций
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,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)
неограниченно продолжаемы.
Замечание. Заключение о неограниченной продолжимости решений дифференциального уравнения легко получить из теоремы , положив
![](data:image/gif;base64,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)
.
Как отмечено выше, существует ряд признаков продолжимости решений. Простейшим из них является признак Винтнера-Еругина, который утверждает, что если в уравнении
![](data:image/gif;base64,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)
функция
![](data:image/gif;base64,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)
определена и непрерывна для всех
![](data:image/gif;base64,R0lGODlhCQAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAGAAoAhAAAAAAAAB0AHQEAAAAAAQAAHh0AMgAdSAAA/x1IbjIAHTVIbjNdgEgcAEgeNFozAERqe0huf1V3al1/f0hzgGxGHXtqRHd3XX9uSGaIiIBdM4iIZqoAAAECAwECAwECAwUaICCOo0UCwvgMRMCIzwlE5EE2pwE4Y1BQohAAOw==)
и
![](data:image/gif;base64,R0lGODlhDQAPAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAKAAgAhAAAAAAAAAEAHR0AAAAdRx0dRwAAqgAyWAAzWh1GbB1IajQ0HTNZf0gcAEcdAERqe1VmZkhzgG5IHWxGHWpIHX9ZM25GM39uSHd3ZmaIiIBdM4iIZv8AAAECAwECAwECAwUcICCOJKAFwhiUwAEg7DUkrNjUgPXi9So6AYUoBAA7)
, как функция двух переменных, то любое решение этого уравнения неограниченно продолжаемо в обе стороны, если только выполняется неравенство
![](data:image/gif;base64,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)
, где
![](data:image/gif;base64,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)
--- функция, удовлетворяющая условию
![](data:image/gif;base64,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)
, где
![](data:image/gif;base64,R0lGODlhEQARAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgANAAwAhQAAAAAAAAAAHQEAHR0AAQEAAB0AAB4AAAAAHgAAMh0AMgAcSAAdRwAAqgAzWwAyWh1GbB1Ibh1GaDMAADMAMzMzADFZfTNZf0cdHVozAFszAFoyAERqe113d1V3d0hzgGxGHX9ZM31ZMXd3XX9/XXtqRHd3ZmaIiIBdM4BzSAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwY5QIBwSCwOQwKOsRhYEimAhRMAEg6mgA9gMnUINYnlZigKXIyEgDpQeBgjxTBRYTQQDwHEMIUPMABBADs=)
--- число. В простейшем случае
![](data:image/gif;base64,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)
, где
![](data:image/gif;base64,R0lGODlhEAARAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgALAAwAhQAAAAAAAAEAAAAAAR0AAB0AHQAAHgAAMwAAMgAcSAAdSAAAqgAA/wIyWAAzWgAzWx1Ibh1GbB1GaB1IajMAADIAATIAADFZfTNdgEgcAEccAUYcAFozAFoyAFszAFgyAF1/f1Vubkhuf0hzgGxGHWpIHX9/XXd3XXdmVXtqRG5uVWaIiIBbM4BzSIiIZqoAAP8AAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwY2QIBwSCRyBINAoCgkHYQUJuAxTBQrQ42DyEIIPd5icsnMDAnMAvFJVAw3RcvwE5gMlXjDaBgEADs=)
--- число, т.е. получаем, что функция
![](data:image/gif;base64,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)
близка к линейной. Ясно, что в этом случае продолжимость всех решений на
![](data:image/gif;base64,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)
легко установить при помощи функций Ляпунова с использованием дифференциальных неравенств, взяв
![](data:image/gif;base64,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)
. Обратное утверждение не всегда верно. Например, для уравнения
![](data:image/gif;base64,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)
условия продолжимости, полученные при помощи функций Ляпунова, запишутся так:
![](data:image/gif;base64,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)
для больших
![](data:image/gif;base64,R0lGODlhEQAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwALABQAhAAAAAAAAAEAHR0AAAAdRx0dRwAAqgAyWAAzWh1GbB1IajQ0HTNZf0gcAEcdAERqe1VmZkhzgG5IHWxGHWpIHX9ZM25GM39uSHd3ZoBdM4iIZv8AAAECAwECAwECAwECAwU7ICCOJBCUZHCiosq2K+u+sxyjcyCMAVEDBwACRhokeLdGKmZZDImACuAyirgCT0dAYbqVfl/v8tUlB0IAOw==)
и
![](data:image/gif;base64,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)
для больших
![](data:image/gif;base64,R0lGODlhEwAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwANABQAhQAAAAAAAB0AHR4AAAAAHgAAMwAAMgAcSAAdSB0dRwAAqh1ISDMAADQeSDNZfzVIbjNbgDNdgEgcAEgdAEkdAFozAEYzRltbW0hIbl1/f0huf0hzgG5GRn9uSHd3XX9/XXtqRGZ3ZmaIiIBdM4BbM4BzSIiIZqoAAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZBQIBwSBwGisjAEUlUMpvLJ8ApnUafVGk2cBgihFlAYWgBXwXJKyNNXBfDEkADSpwY3tcLOwGgMJUlAwRYV3+FSUEAOw==)
. Понятно, что, положив
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,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)
получим, на основании теоремы , вывод о продолжимости всех решений уравнений
![](data:image/gif;base64,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)
. Но критерий Винтнера-Еругина не выполняется за счет
![](data:image/gif;base64,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)
.
Рассмотрим уравнение
![](data:image/gif;base64,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)
эквивалентное системе
![](data:image/gif;base64,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)
Теорема
Пусть
![](data:image/gif;base64,R0lGODlhHAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAXAA8AhQAAAAAAAB4AHh0AHQEAAAAAAQAAHQAAHgAAMx0AMx0AMgAAMgEAMgAdSAAdRwAA/wAzWgAzWx1Ibh1GbB1IajIAHTIAATMAADMAHTMAMzVIbjNdgDNbgEgdAUYcAFUAAEgcAEcdAEgeNFozAFkzAl1/f1V3d0Rqe1V3f0huf113d1VublV3akhzgG5IHWxGHX9ZM25bNXd3VX9/XX93VXtqRGZmVXd3XX9uSHd3ZmaIiIBbM4BdM4BzSIiIZqoAAAZsQIBwSCwaj8ZMElmEIZAC5lDJTEgBkmJtcBpCiJ0AYQKoFEeEQmCoGFoogBcg9jwXL0JPREiC14lmRBdkBkIXXy9/Qw13cWoLRIoAIEZ4AAxDUVdsQiEBAQ5DI0UBB0QvX0wYm1ealRusVExBADs=)
--- непрерывная на всех
![](data:image/gif;base64,R0lGODlhIQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAdAAwAhQAAAAAAAB0AHQEAAAAAAR0AAB4AAAAAHgAAMwAAMh0AMgAcSAAdSQAAVQAdSAAdRwEdSAAAqgAA/wAzWwAzWh1GbB1Ibh1IajMAADIAHTFZfTNZfzVIbjNbgDNdgEgcAEgdAEgeNFozAF1/f0Rqe1VmZkhuf113d1V3akhzgGpGHWpIHWxGHX9ZM39/XXtqRH9uSHd3VXd3XW5uVWaIiIBbM4BdM4iIZqoAAP8AAAECAwECAwECAwECAwECAwECAwZiQIBwSCwaj8jkURUIKJ9FhBBTfB2dys5wQRQkA4yjdzgWDQgBT7KQINakQ6pQBMVgh/CpVmhKGtpFb0QFQw5IAQ9JY0JjH0crUAAbhUIKACGRRhBTQwEHKUUrTaNNFKFNQ0EAOw==)
функция, а функции
![](data:image/gif;base64,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)
,
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,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)
удовлетворяют условиям:
а)
![](data:image/gif;base64,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)
--- ограниченная для всех
![](data:image/gif;base64,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)
, где
![](data:image/gif;base64,R0lGODlhEQARAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgANAAwAhQAAAAAAAB0AAQAAAQEAAAAAHR4AAAAAHgAAMwAcRgAcSAAAqgAA/wAzWgAyWh1Ibh1IajMAADIAHTFZfTNGbjNbgEgcAEgdAEccAUcdAFgyAFszAEhZfVVmd11/f0huf0Rqe1V3d0hzgGxGHX9ZM3tqRH9/XXdmVX9uSG5uVWaIiIBdM4BzSIiIZqoAAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZAQIBwSCwCSoKAMjApagaN4SqQGJIGj+KK4BBaEEbApSCMhIWBsuIcqIjPALJQXsQUwcRNWDK0DCkABkoHREsAQQA7)
--- некоторое ограниченное множество, содержащее начало координат,
б)
![](data:image/gif;base64,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)
при
![](data:image/gif;base64,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)
,
в)
![](data:image/gif;base64,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)
--- непрерывная и непрерывно дифференцируемая по
![](data:image/gif;base64,R0lGODlhDQAPAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAKAAgAhAAAAAAAAAEAHR0AAAAdRx0dRwAAqgAyWAAzWh1GbB1IajQ0HTNZf0gcAEcdAERqe1VmZkhzgG5IHWxGHWpIHX9ZM25GM39uSHd3ZmaIiIBdM4iIZv8AAAECAwECAwECAwUcICCOJKAFwhiUwAEg7DUkrNjUgPXi9So6AYUoBAA7)
функция и
![](data:image/gif;base64,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)
,
![](data:image/gif;base64,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)
для всех
![](data:image/gif;base64,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)
. Тогда все решения системы или уравнения неограниченно продолжаемы.
Доказательство
В самом деле, возьмем функцию
![](data:image/gif;base64,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)
Оценивая ее производную в силу системы при
![](data:image/gif;base64,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)
(для
![](data:image/gif;base64,R0lGODlhEQAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwALABQAhAAAAAAAAAEAAAAAHQAzWjFZfTNdgEkdAFszAFgyAFluf11/f0hzgGpIHXtVVX9uWYiIZqoAAP8AAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwUvICCOJBCUZHCiosq2K+u+sxyj86EKA4waPtoNOKrhVoWjSRUgFG8lYxSaoj5fphAAOw==)
, вообще говоря больших), перейдем к неравенству
![](data:image/gif;base64,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)
которое, очевидно, в силу леммы , не имеет ни одного положительного решения с конечным временем определения. Воспользовавшись теоремой , приходим к требуемому заключению.
Замечание. Воспользовавшись этой теоремой, легко получить вывод о продолжимости всех решений уравнения
![](data:image/gif;base64,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)
и уравнения
![](data:image/gif;base64,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)
В самом деле, при выполнении всех условий теоремы , полагая
![](data:image/gif;base64,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)
в первом случае и
![](data:image/gif;base64,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)
--- во втором, легко получаем
Следствие. Если в уравнении функции
![](data:image/gif;base64,R0lGODlhHAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAXAA8AhQAAAAAAAB4AHh0AHQEAAAAAAQAAHQAAHgAAMx0AMx0AMgAAMgEAMgAdSAAdRwAA/wAzWgAzWx1Ibh1GbB1IajIAHTIAATMAADMAHTMAMzVIbjNdgDNbgEgdAUYcAFUAAEgcAEcdAEgeNFozAFkzAl1/f1V3d0Rqe1V3f0huf113d1VublV3akhzgG5IHWxGHX9ZM25bNXd3VX9/XX93VXtqRGZmVXd3XX9uSHd3ZmaIiIBbM4BdM4BzSIiIZqoAAAZsQIBwSCwaj8ZMElmEIZAC5lDJTEgBkmJtcBpCiJ0AYQKoFEeEQmCoGFoogBcg9jwXL0JPREiC14lmRBdkBkIXXy9/Qw13cWoLRIoAIEZ4AAxDUVdsQiEBAQ5DI0UBB0QvX0wYm1ealRusVExBADs=)
,
![](data:image/gif;base64,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)
непрерывны по
![](data:image/gif;base64,R0lGODlhCQAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAGAAoAhAAAAAAAAB0AHQEAAAAAAQAAHh0AMgAdSAAA/x1IbjIAHTVIbjNdgEgcAEgeNFozAERqe0huf1V3al1/f0hzgGxGHXtqRHd3XX9uSGaIiIBdM4iIZqoAAAECAwECAwECAwUaICCOo0UCwvgMRMCIzwlE5EE2pwE4Y1BQohAAOw==)
и
![](data:image/gif;base64,R0lGODlhDwARAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAKAAsAhQAAAAAAAB0AHR4AAAAAHgAAMwAAMgAcSAAdSB0dRwAAqh1ISDMAADQeSDNZfzVIbjNbgDNdgEgcAEgdAEkdAFozAEYzRltbW0hIbl1/f0huf0hzgG5GRn9uSHd3XX9/XXtqRGZ3ZmaIiIBdM4BbM4BzSIiIZqoAAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwYkQIBwSBRWAochgkgqFImC55ABAXCeDOlwoZ0YtGBK5DkgbJ5BADs=)
соответственно и
![](data:image/gif;base64,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)
для больших
![](data:image/gif;base64,R0lGODlhEwAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwANABQAhQAAAAAAAB0AHR4AAAAAHgAAMwAAMgAcSAAdSB0dRwAAqh1ISDMAADQeSDNZfzVIbjNbgDNdgEgcAEgdAEkdAFozAEYzRltbW0hIbl1/f0huf0hzgG5GRn9uSHd3XX9/XXtqRGZ3ZmaIiIBdM4BbM4BzSIiIZqoAAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZBQIBwSBwGisjAEUlUMpvLJ8ApnUafVGk2cBgihFlAYWgBXwXJKyNNXBfDEkADSpwY3tcLOwGgMJUlAwRYV3+FSUEAOw==)
, а функция
![](data:image/gif;base64,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)
для больших
![](data:image/gif;base64,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)
то все решения этого уравнения продолжимы на
![](data:image/gif;base64,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)
.
Следствие. Если в уравнении () функции
![](data:image/gif;base64,R0lGODlhHAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAXAA8AhQAAAAAAAB4AHh0AHQEAAAAAAQAAHQAAHgAAMx0AMx0AMgAAMgEAMgAdSAAdRwAA/wAzWgAzWx1Ibh1GbB1IajIAHTIAATMAADMAHTMAMzVIbjNdgDNbgEgdAUYcAFUAAEgcAEcdAEgeNFozAFkzAl1/f1V3d0Rqe1V3f0huf113d1VublV3akhzgG5IHWxGHX9ZM25bNXd3VX9/XX93VXtqRGZmVXd3XX9uSHd3ZmaIiIBbM4BdM4BzSIiIZqoAAAZsQIBwSCwaj8ZMElmEIZAC5lDJTEgBkmJtcBpCiJ0AYQKoFEeEQmCoGFoogBcg9jwXL0JPREiC14lmRBdkBkIXXy9/Qw13cWoLRIoAIEZ4AAxDUVdsQiEBAQ5DI0UBB0QvX0wYm1ealRusVExBADs=)
,
![](data:image/gif;base64,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)
и
![](data:image/gif;base64,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)
удовлетворяют условиям:
а)
![](data:image/gif;base64,R0lGODlhHAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAXAA8AhQAAAAAAAB4AHh0AHQEAAAAAAQAAHQAAHgAAMx0AMx0AMgAAMgEAMgAdSAAdRwAA/wAzWgAzWx1Ibh1GbB1IajIAHTIAATMAADMAHTMAMzVIbjNdgDNbgEgdAUYcAFUAAEgcAEcdAEgeNFozAFkzAl1/f1V3d0Rqe1V3f0huf113d1VublV3akhzgG5IHWxGHX9ZM25bNXd3VX9/XX93VXtqRGZmVXd3XX9uSHd3ZmaIiIBbM4BdM4BzSIiIZqoAAAZsQIBwSCwaj8ZMElmEIZAC5lDJTEgBkmJtcBpCiJ0AYQKoFEeEQmCoGFoogBcg9jwXL0JPREiC14lmRBdkBkIXXy9/Qw13cWoLRIoAIEZ4AAxDUVdsQiEBAQ5DI0UBB0QvX0wYm1ealRusVExBADs=)
непрерывна для
![](data:image/gif;base64,R0lGODlhIQATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAdAAwAhQAAAAAAAB0AHQEAAAAAAR0AAB4AAAAAHgAAMwAAMh0AMgAcSAAdSQAAVQAdSAAdRwEdSAAAqgAA/wAzWwAzWh1GbB1Ibh1IajMAADIAHTFZfTNZfzVIbjNbgDNdgEgcAEgdAEgeNFozAF1/f0Rqe1VmZkhuf113d1V3akhzgGpGHWpIHWxGHX9ZM39/XXtqRH9uSHd3VXd3XW5uVWaIiIBbM4BdM4iIZqoAAP8AAAECAwECAwECAwECAwECAwECAwZiQIBwSCwaj8jkURUIKJ9FhBBTfB2dys5wQRQkA4yjdzgWDQgBT7KQINakQ6pQBMVgh/CpVmhKGtpFb0QFQw5IAQ9JY0JjH0crUAAbhUIKACGRRhBTQwEHKUUrTaNNFKFNQ0EAOw==)
,
б)
![](data:image/gif;base64,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)
ограничена для больших
![](data:image/gif;base64,R0lGODlhEQAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwALABQAhAAAAAAAAAEAHR0AAAAdRx0dRwAAqgAyWAAzWh1GbB1IajQ0HTNZf0gcAEcdAERqe1VmZkhzgG5IHWxGHWpIHX9ZM25GM39uSHd3ZoBdM4iIZv8AAAECAwECAwECAwECAwU7ICCOJBCUZHCiosq2K+u+sxyjcyCMAVEDBwACRhokeLdGKmZZDImACuAyirgCT0dAYbqVfl/v8tUlB0IAOw==)
,
в)
![](data:image/gif;base64,R0lGODlhOwAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgA2AA8AhgAAAAAAAB4AHh0AAAEAAB0AHR4AAAAAHgAAMx0AMx0AMgAAMgAcSAAdSQAAVR0dSQAdSAAdRwEdSB0dRwAAqgAA/wAzWwAzWh0zWwAyWB1ISB1GbB1Ibh1IajMAADIAHTMAHTMAMzIAMjQeSDFZfTNZfzVIbjNbgDNdgEgcAEgdAEkdAEceM0UeM1ozAFgyAkYzRk9HHEhOM1tbW0hIblV7VV1/f1V3d0Rqe1V3f1VmZkhuf113d1VubkhzgGpGHWpIHW5IHWxGHX9ZM31ZMW5GRnd3VX9/XX93VXtqRH9uSHd3XWZmVW5uVWZ3ZmaIiIBbM4BdM4BzSIiIZqoAAP8AAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwfrgACCg4SFhoeIiYqLgiGKjoyJPwEBkYMIjAI4hxuLQ5gAHpaQjAmIARaJKYQMhEkDHAABBCQALpYAQYlRAQ2HBYNKBTuXgg+5mB+GLgGtghCDCosDC4WggqIAn4JCg8DXhFDggx4nih6VhODlACmxACyXMePeh9mHBtWG4AOCwIIYBsWih81cEUIeOhEaEiBCon8AkgwD8K+bIFAEQ9kzdGGRCkLQNBLSB0AZIg2FkuAiFIUcIQMEKHUopLCQCpKDOhICQqknJZ2DeKYjdAvRJkakVioSkUhAoRUoCt1TqgioIgMHfBRKStVQIAA7)
для больших
![](data:image/gif;base64,R0lGODlhEwAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwANABQAhQAAAAAAAB0AHR4AAAAAHgAAMwAAMgAcSAAdSB0dRwAAqh1ISDMAADQeSDNZfzVIbjNbgDNdgEgcAEgdAEkdAFozAEYzRltbW0hIbl1/f0huf0hzgG5GRn9uSHd3XX9/XXtqRGZ3ZmaIiIBdM4BbM4BzSIiIZqoAAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZBQIBwSBwGisjAEUlUMpvLJ8ApnUafVGk2cBgihFlAYWgBXwXJKyNNXBfDEkADSpwY3tcLOwGgMJUlAwRYV3+FSUEAOw==)
,
г)
![](data:image/gif;base64,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)
непрерывна и
![](data:image/gif;base64,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)
для больших
![](data:image/gif;base64,R0lGODlhEwAbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwANABQAhQAAAAAAAB0AHR4AAAAAHgAAMwAAMgAcSAAdSB0dRwAAqh1ISDMAADQeSDNZfzVIbjNbgDNdgEgcAEgdAEkdAFozAEYzRltbW0hIbl1/f0huf0hzgG5GRn9uSHd3XX9/XXtqRGZ3ZmaIiIBdM4BbM4BzSIiIZqoAAAECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwECAwZBQIBwSBwGisjAEUlUMpvLJ8ApnUafVGk2cBgihFlAYWgBXwXJKyNNXBfDEkADSpwY3tcLOwGgMJUlAwRYV3+FSUEAOw==)
, то все решения уравнения неограниченно продолжимы вправо.
Пример. Очевидно, что всем условиям продолжимости удовлетворяет уравнение