Existence and concentration of solution for a class of fractional elliptic equation in ℝ^N via penalization method

2015/08/17 by Claudianor O. Alves, Alves, Claudianor O., Olimpio H. Miyagaki +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1508.03964

arxiv created 2015/08/17 · arxiv updated 2015/08/18

Abstract

In this paper, we study the existence and concentration of positive solution for the following class of fractional elliptic equation ε^2s (-Δ)^su+V(z)u=f(u) in ℝ^N, where ε is a positive parameter, f has a subcritical growth, V possesses a local minimum, N > 2s, s ∈ (0,1), and (-Δ)^su is the fractional laplacian.

Cited by

• Existence and concentration phenomenon of multiple solutions for the fractional logarithmic Schrödinger-Poisson system via penalization method
• Concentration phenomena for fractional elliptic equations involving exponential critical growth

Related

• Concentration phenomena for fractional elliptic equations involving exponential critical growth
• A critical nonlinear fractional elliptic equation with saddle-like potentical in ℝ^N
• Fractional elliptic problems with critical growth in the whole of \Rⁿ
• Existence and concentration of solutions for a fractional Schrodinger equations with sublinear nonlinearity
• Multiplicity of solutions for a class of fractional elliptic problem with critical exponential growth and nonlocal Neumann condition