Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900312 | Journal of Mathematical Analysis and Applications | 2018 | 18 Pages |
Abstract
In this paper, we deal with the existence, multiplicity and asymptotic behavior of solutions for the following stationary Kirchhoff problems involving the p-Laplacian:âM(â«Î©|âu|pdx)Îpu=λf(x,u)+|u|pââ2uinΩ,u=0 onâΩ, where Ω is a bounded smooth domain of RN, M:R0+âR0+ is a continuous function satisfying some extra assumptions. By using the mountain pass theorem, the existence of solutions is obtained. By applying an abstract critical point theorem based on the cohomological index, we prove the existence of multiple solutions for the above problem, when parameter λ belongs to some left neighborhood of the eigenvalue of the nonlinear operator âââuâ(θâ1)pÎp, where p
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Li Wang, Kun Xie, Binlin Zhang,