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Об асимптотической классификации решений нелинейных уравнений третьего и четвертого порядков со степенной нелинейностью

Авторы: Асташова И.В. Опубликовано: 15.04.2015
Опубликовано в выпуске: #2(59)/2015  
DOI: 10.18698/1812-3368-2015-2-3-25

 
Раздел: Математика | Рубрика: Дифференциальные уравнения, динамические системы и оптимальное управление  
Ключевые слова: нелинейное дифференциальное уравнение высокого порядка, асимптотическое поведение решений, качественные свойства, асимптотическая классификация решений

Исследовано асимптотическое поведение всех решений нелинейных дифференциальных уравнений типа Эмдена - Фаулера третьего и четвертого порядков. Приведены ранее полученные автором настоящей статьи результаты. Уравнение n-го порядка сведено к системе на (п - 1)-мерной сфере. С помощью исследования асимптотического поведения всех возможных траекторий системы получена асимптотическая классификация решений исходного уравнения.

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