, Volume 27, Issue 1-2, pp 107-116
Date: 20 Mar 2008

Homoclinic orbits of two classes of fourth order semilinear differential equations with periodic nonlinearity

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Abstract

This paper discusses the existence of homoclinic solutions for two classes of fourth order periodic semilinear differential equations u''''+pu″+a(x)uV u (x,u)=0 by Ambrosetti–Rabinowitz’s Mountain Pass Lemma and Lion’s concentration-compactness argument, where V(x,u) is a positive and superquadratic potential or an indefinite polynomial one with periodicity in x.

Supported by National Science Foundation of China (1037100), KOSEF in 2005, and “985 Engineer” Project of Central University for Nationalities (CUN 985-3-3).