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Abstract
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Abstract and Applied Analysis
Volume 7 (2002), Issue 1, Pages 1-27
doi:10.1155/S108533750200074X

Existence problems for homoclinic solutions

Cezar Avramescu

Department of Mathematics, University of Craiova, 13 AI Cuza street, Craiova 1100, Romania

Abstract

The problem x˙=f(t,x), x(−∞)=x(+∞), where x(±∞):=limt→±∞x(t)∈ℝn, is considered. Some existence results for this problem are established using the fixed point method and topological degree theory.