Asymmetric critical p-Laplacian problems

作者：Perera, Kanishka; Yang, Yang; Zhang, Zhitao^*

来源：Calculus of Variations and Partial Differential Equations, 2018, 57(5): 131.

DOI：10.1007/s00526-018-1416-9

• AMBROSETTI-PRODI PROBLEM
• ELLIPTIC-EQUATIONS
• NONLINEARITY
• LINKING

We obtain nontrivial solutions for two types of asymmetric critical p-Laplacian problems with Ambrosetti-Prodi type nonlinearities in a smooth bounded domain in R-N, N >= 2. For 1 < p < N, we consider an asymmetric problem involving the critical Sobolev exponent p* = Np/(N - p). In the borderline case p = N, we consider an asymmetric critical exponential nonlinearity of the Trudinger-Moser type. In the absence of a suitable direct sum decomposition, we use a linking theorem based on the Z(2)-cohomological index to prove existence of solutions.

• 单位
  中国科学院数学与系统科学研究院; 中国科学院大学; 江南大学