Electron. J. Diff. Equ., Vol. 2010(2010), No. 165, pp. 1-12.

Continuability and boundedness of solutions to nonlinear second-order differential equations

Lianwen Wang, Rhonda McKee, Larysa Usyk

Abstract:
Continuability, boundedness, and monotonicity of solutions for a class of second-order nonlinear differential equations are discussed. It is proved that all solutions are eventually monotonic and can be extended to infinity under some natural assumptions. Moreover, necessary and sufficient conditions for boundedness of all solutions are established. The results obtained have extended and improved some analogous existing ones.

Submitted February 27, 2010. Published November 17, 2010.
Math Subject Classifications: 34C11, 34C12.
Key Words: Nonlinear differential equations; second order; boundedness; monotonicity; continuability; asymptotic properties.

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Lianwen Wang
Department of Mathematics and Computer Science
University of Central Missouri
Warrensburg, MO 64093, USA
email: lwang@ucmo.edu
Rhonda McKee
Department of Mathematics and Computer Science
University of Central Missouri
Warrensburg, MO 64093, USA
email: mckee@ucmo.edu
  Larysa Usyk
Department of Mathematics and Computer Science
University of Central Missouri
Warrensburg, MO 64093, USA
email: lmu58230@ucmo.edu

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