Electron. J. Diff. Eqns., Vol. 2004(2004), No. 18, pp. 1-12.

Existence of solutions to second order ordinary differential equations having finite limits at $\pm\infty$

Cezar Avramescu & Cristian Vladimirescu

In this article, we study the boundary-value problem
 \ddot{x}=f(t,x,\dot{x}), \quad x(-\infty )=x(+\infty ), \quad
 \dot{x}(-\infty) = \dot{x}(+\infty ) =0\,.
Under adequate hypotheses and using the Bohnenblust-Karlin fixed point theorem for multivalued mappings, we establish the existence of solutions.

Submitted February 14, 2003. Published February 9, 2004.
Math Subject Classifications: 34B15, 34B40, 34C37, 54C60.
Key Words: Nonlinear boundary-value problem, set-valued mappings, boundary-value problems on infinite intervals.

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Cezar Avramescu
Centre for Nonlinear Analysis and its Applications
University of Craiova, Al.I. Cuza Street, No. 13
Craiova RO-200585, Romania
email: zarce@central.ucv.ro   cezaravramescu@hotmail.com
Cristian Vladimirescu
Department of Mathematics, University of Craiova
Al.I. Cuza Street, No. 13
Craiova RO-200585, Romania
email: cvladi@central.ucv.ro   vladimirescucris@hotmail.com

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