Mathematics and System Engineering Faculty Publications

Document Type

Article

Publication Title

Advanced Nonlinear Studies

Abstract

This article deals with existence of solutions to the following fractional p -Laplacian system of equations: (- Δp)s u = |u| p s∗-2 u + γ α/ps∗ |u|α-2 u |v|β in ω, (-Δp)s v = |v| ps∗ - 2 v + γ β /ps∗ |v|β - 2 v |u|α in ω, where s ϵ (0, 1), p ϵ (1, ∞) with N > sp, α, β > 1 such that α + β = ps∗ := Np/ N - sp and ω = ℝN or smooth bounded domains in ℝN. When ω = ℝN and γ = 1, we show that any ground state solution of the aforementioned system has the form (λ U, τ λ V) for certain τ > 0 and U and V are two positive ground state solutions of (- Δ p)s u = |u|ps∗ - 2 u in ℝN. For all γ > 0, we establish existence of a positive radial solution to the aforementioned system in balls. When ω = ℝN, we also establish existence of positive radial solutions to the aforementioned system in various ranges of γ. © 2023 the author(s), published by De Gruyter.

DOI

10.1515/ans-2023-0103

Publication Date

2023

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