Kirchhoff systems involving fractional p-Laplacian and singular nonlinearity
Date
2022-11-21
Authors
Kratou, Mouna
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this work we consider the fractional Kirchhoff equations with singular nonlinearity,
M(∫ℝ2N |u(x) - u(y)|p/|x-y|N+sp dxdy) (-∆)s pu
= λα(x)|u|q-2u + 1-α/2-α-β c(x)|u|-α|v|1-β, in Ω,
M(∫ℝ2N |v(x)-v(y)|p/|x-y|N+sp dx/dy) (-∆)s pv
= μb(x)|v|q-2v + 1-β/2-α-β c(x)|u|1-α|v|-β, in Ω,
u = v = 0, in ℝN \ Ω,
where Ω is a bounded domain in ℝN with smooth boundary, N > ps, s in (0, 1), 0<α<1, 0<β<1, 2-α-β<p≤ pθ<q<p*s, p*s=Np/(N-sp) is the fractional Sobolev exponent, λ, μ are two parameters, a, b, c in C(overlineΩ) are non-negative weight functions, M(t)=k+ltθ-1 with k>0, l,θ≥1, and (-Δ)sp is the fractional p-laplacian operator. We prove the existence of multiple non-negative solutions by studying the nature of the Nehari manifold with respect to the parameters λ and μ.
Description
Keywords
Kirchhoff-type equations, Fractional p-Laplace operator, Nehari manifold, Singular elliptic system, Multiple positive solutions
Citation
Kratou, M. (2022). Kirchhoff systems involving fractional p-Laplacian and singular nonlinearity. <i>Electronic Journal of Differential Equations, 2022</i>(77), pp. 1-15.
Rights
Attribution 4.0 International