Principal eigenvalue and positive solutions for Fractional P-Q Laplace operator in quantum field theory

2020/06/05 by Nguyen, Thanh-Hieu, Vo, Hoang-Hung
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.03233

Abstract

This article deals with the existence and non-existence of positive solutions for the eigenvalue problem driven by nonhomogeneous fractional p& q Laplacian operator with indefinite weights (-Δ_p)^αu + (-Δ_q)^βu = λ[a(x) |u|^p-2u + b(x) |u|^q-2u ] \textrmin Ø, where Ø is a smooth bounded domain in \R^N extended by zero outside. When Ø=\R^N and b≡0, we further show that there exists a continuous family of the eigenvalue if 1

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