Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 18, pp. 1-12.
Title: Existence of solutions to second order ordinary differential
equations having finite limits at +/- infinity
Authors: Cezar Avramescu (Univ. of Craiova, Romania)
Cristian Vladimirescu (Univ. of Craiova, Romania)
Abstract:
In this article, we study the boundary-value problem
$$
\ddot{x}=f(t,x,\dot{x}), \quad x(-\infty )=x(+\infty), \quad
\dot{x}(-\infty) = \dot{x}(+\infty )\,.
$$
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