Asymmetric critical p-Laplacian problems

2016/02/02 by Kanishka Perera, Yang Yang, Perera, Kanishka +3 · 1 citation
Computer Science · Mathematics · #35B33 (Primary) #35J20 (Secondary) #35J92 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1602.01071

openalex publication_date 2016/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain nontrivial solutions for two types of critical p-Laplacian problems with asymmetric nonlinearities in a smooth bounded domain in \mathbb R^N, N ≥ 2. For 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 \mathbb Z₂-cohomological index to obtain our solutions.

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• Nontrivial solutions for nonlinear problems driven by a superposition of fractional p-Laplacians with Neumann boundary conditions

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