EMIS ELibM Electronic Journals Journal of Applied Analysis
Vol. 1, No. 1, pp. 83-93 (1995)

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The existence of homoclinic solutions for hyperbolic equations

A. Nowakowski and A. Rogowski

Institute of Mathematics
Lodz University
ul. Stefana Banacha 22
90-238 Lodz, Poland
e-mail: annowako@krysia.uni.lodz.pl,

Abstract: Studying homoclinic solutions of equations is one of the steps to go deeper in the understanding of dynamics. As it is known to the authors there are no papers studying homoclinic solutions of hyperbolic systems. In the paper we present a new variational method general enough to treat the problem of the existence of homoclinic solutions for the following semi-linear wave equation: $x_{tt}(t,y)-x_{yy}(t,y)+g(t,y,x(t,y))=0$ for $0Keywords: Hyperbolic P.D.E., sublinear nonlinearity, superlinear nonlinearity, 2D-systems, homoclinic solutions, variational method, duality

Classification (MSC2000): 35B, 35L

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