Journal of Applied Mathematics

Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions

Lianwen Wang and Rhonda McKee

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 313725, 14 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495214

Digital Object Identifier
doi:10.1155/2012/313725

Mathematical Reviews number (MathSciNet)
MR2948155

Zentralblatt MATH identifier
1255.34033

Citation

Wang, Lianwen; McKee, Rhonda. Nonoscillatory Solutions of Second-Order Differential Equations without Monotonicity Assumptions. J. Appl. Math. 2012 (2012), Article ID 313725, 14 pages. doi:10.1155/2012/313725. https://projecteuclid.org/euclid.jam/1355495214


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