Existence of positive solution for a class of nonlocal elliptic problems in the half space with a hole

2021/04/27 by Xing Yi, Yi, Xing
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2104.12940

openalex publication_date 2021/04/27 · openalex created_date 2021/05/10 · openalex updated_date 2026/07/28

Abstract

This work concerns with the existence of solutions for the following class of nonlocal elliptic problems amp;amp;\(-Δ)^s u+u=|u|^p-2 u \text in Ω_r
u ≥ 0 \text in Ω_r \text and u ≠ 0
u=0 ℝ^N \backslash Ω_r., involving the fractional Laplacian operator (-Δ)^s, where s ∈(0,1), N>2 s, Ω_r is the half space with a hole in ℝ^N and p ∈(2,2_s^*) . The main technical approach is based on variational and topological methods.

Citations

• Uniqueness of positive solutions of Δu−u+up=0 in Rn

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