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2012 Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions
Lianwen Wang, Rhonda McKee
J. Appl. Math. 2012: 1-14 (2012). DOI: 10.1155/2012/313725


The continuability, boundedness, monotonicity, and asymptotic properties of nonoscillatory solutions for a class of second-order nonlinear differential equations [ p ( t ) h ( x ( t ) ) f ( x ( t ) ) ] = q ( t ) g ( x ( t ) ) are discussed without monotonicity assumption for function g. It is proved that all solutions can be extended to infinity, are eventually monotonic, and can be classified into disjoint classes that are fully characterized in terms of several integral conditions. Moreover, necessary and sufficient conditions for the existence of solutions in each class and for the boundedness of all solutions are established.


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Lianwen Wang. Rhonda McKee. "Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions." J. Appl. Math. 2012 1 - 14, 2012.


Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1255.34033
MathSciNet: MR2948155
Digital Object Identifier: 10.1155/2012/313725

Rights: Copyright © 2012 Hindawi

Vol.2012 • 2012
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