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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)u−V 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.

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Authors and Affiliations

  1. Mathematics Department, Central University for Nationalities, Beijing, 100081, China

    Chengyue Li

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  1. Chengyue Li
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Correspondence to Chengyue Li.

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

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Li, C. Homoclinic orbits of two classes of fourth order semilinear differential equations with periodic nonlinearity. J. Appl. Math. Comput. 27, 107–116 (2008). https://doi.org/10.1007/s12190-008-0045-4

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  • DOI: https://doi.org/10.1007/s12190-008-0045-4

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