Non-homogeneous (p₁,p₂)-fractional Laplacian systems with lack of compactness

2021/07/13 by Debangana Mukherjee, Mukherjee, Debangana, Tuhina Mukherjee +1
Mathematics · #35J20 #45G05 #49J35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Primary 35R11 #Spectral Theory in Mathematical Physics #secondary 47G20

paper · pdf · doi:10.48550/arxiv.2107.06204

openalex publication_date 2021/07/13 · openalex created_date 2021/07/19 · openalex updated_date 2026/07/28

Abstract

The present paper studies the existence of weak solutions for the following type of non-homogeneous system of equations (S) \\beginaligned (-Δ)s1p1 u amp;=u|u|α-1|v|β+1+f1(x) in Ω,
(-Δ)s2p2 v amp;=|u|α+1v|v|β-1+f2(x) in Ω,
u=v amp;= 0 in ℝN ∖ Ω,
\endaligned . where Ω⊂ ℝN is smooth bounded domain, s1,s2 ∈ (0,1), 1max\p1s1,p2s2\, α>-1 and β>-1. We employ the variational techniques where the associated energy functional is minimized over Nehari manifold set while imposing appropriate bound on dual norms of f1,f2.

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