Multiple solutions for a fourth-order nonlinear elliptic problem which is superlinear at +∞ and linear at −∞
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
Boundary Value Problems 2014, 2014:12 doi:10.1186/1687-2770-2014-12Published: 10 January 2014
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.