an:07053621
Zbl 1421.35132
Ho, Ky; Kim, Yun-Ho; Sim, Inbo
Existence results for Schr??dinger \(p(\cdot)\)-Laplace equations involving critical growth in \(\mathbb{R}^N$
EN
Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 182, 20-44 (2019).
00432542
2019
j
35J62 35J10 35B33 35J35 46E35
quasilinear equation with \(p(\cdot)\)-Laplacian; weighted variable exponent Sobolev spaces; concentration-compactness principle
Summary: We establish some existence results for Schr??dinger \(p(\cdot)\)-Laplace equations in \(\mathbb{R}^N\) with various potentials and critical growth of nonlinearity that may occur on some nonempty set, although not necessarily the whole space \(\mathbb{R}^N\). The proofs are mainly based on concentration-compactness principles in a suitable weighted variable exponent Sobolev space and its imbeddings.