Existence results for Schrödinger p(x)-Laplace equations involving critical growth in ℝ^N

2018/07/11 by Ky Ho, Yun-Ho Kim, Ho, Ky +3
Computer Science · Mathematics · #35B33 #35J20 #35J25 #35J62 #35J70 #46E35 #47J10 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1807.03961

openalex publication_date 2018/07/11 · openalex created_date 2018/07/19 · openalex updated_date 2026/07/28

Abstract

We establish some existence results for Schrödinger p(x)-Laplace equations in ℝ^N with various potentials and critical growth of nonlinearity that may occur on some nonempty set, although not necessarily the whole space ℝ^N. The proofs are mainly based on concentration-compactness principles in a suitable weighted variable exponent Sobolev space and its imbeddings.

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