Multiple sign-changing solutions to semilinear elliptic resonant problems

作者：Li Fuyi^*; Li Yuhua

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 72(9-10): 3820-3827.

DOI：10.1016/j.na.2010.01.018

• Sign-changing solution
• Elliptic resonant problem
• Topological degree
• Critical group

In this paper, we use the topological degree theory and the critical groups to investigate the elliptic equation -Delta u = f(x, u) in Omega and subject to u = 0 on partial derivative Omega, and establish a multiple solutions theorem which guarantees that this problem has at least six nontrivial solutions under some resonant conditions. If this problem has only finitely many solutions then, of these solutions, there are two positive solutions, two negative solutions and two sign-changing solutions.

• 出版日期2010-5-1
• 单位山西大学