Journal of Applied Mathematics and Computing

, Volume 27, Issue 1, pp 107–116

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

Article

DOI: 10.1007/s12190-008-0045-4

Cite this article as:
Li, C. J. Appl. Math. Comput. (2008) 27: 107. doi:10.1007/s12190-008-0045-4

Abstract

This paper discusses the existence of homoclinic solutions for two classes of fourth order periodic semilinear differential equations u''''+pu″+a(x)uVu(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.

Keywords

Homoclinic orbit Fisher–Kolmogorov equation Mountain Pass Lemma 

Mathematics Subject Classification (2000)

58E05 34C37 70H05 

Copyright information

© KSCAM and Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mathematics DepartmentCentral University for NationalitiesBeijingChina