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Open Access Research

Multiple solutions for a fourth-order nonlinear elliptic problem which is superlinear at +∞ and linear at −∞

Ruichang Pei12* and Jihui Zhang2

Author Affiliations

1 School of Mathematics and Statistics, Tianshui Normal University, Tianshui, 741001, P.R. China

2 School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing, 210097, P.R. China

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Boundary Value Problems 2014, 2014:12  doi:10.1186/1687-2770-2014-12

Published: 10 January 2014

Abstract

We consider a semilinear fourth-order elliptic equation with a right-hand side nonlinearity which exhibits an asymmetric growth at +∞ and at −∞. Namely, it is linear at −∞ and superlinear at +∞. Combining variational methods with Morse theory, we show that the problem has at least two nontrivial solutions, one of which is negative.

Keywords:
fourth-order elliptic boundary value problems; multiple solutions; critical groups; Morse theory