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Qualitative behavior of solutions of a third order nonlinear differential equation
Author(s) -
Graef John R.,
Remili Moussadek
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600491
Subject(s) - mathematics , nonlinear system , class (philosophy) , order (exchange) , differential equation , third order , mathematical analysis , differential (mechanical device) , thermodynamics , computer science , philosophy , physics , theology , finance , quantum mechanics , artificial intelligence , economics
In this paper the oscillatory and asymptotic behavior of solutions of a class of nonlinear third order differential equations of the form( a ( t ) x ′ ′ + b ( t ) x ′ + p ( t ) x ) ′ + p ( t ) x ′ + q ( t ) f ( x ) = 0 are studied. Results on the square integrability of solutions and their derivatives are obtained. An example to illustrate the results is included and directions for future research are indicated.