Multiple solutions for a fourth-order nonlinear elliptic problem which is superlinear at plus infinity and linear at -infinity

作者：Pei, Ruichang^*; Zhang, Jihui

来源：Boundary Value Problems, 2014, 2014(1): 12.

DOI：10.1186/1687-2770-2014-12

• fourth-order elliptic boundary value problems
• multiple solutions
• critical groups
• Morse theory

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

• 出版日期2014-1-10
• 单位天水师范学院; 南京师范大学