On Dirichlet problem for fractionalp-Laplacian with singular non-linearity

Abstract

In this article, we study the following fractional p-Laplacian equation with critical growth singular nonlinearitywhere Ω is a bounded domain in R n with smooth boundary ∂Ω, n > sp, s ∈ (0, 1), λ > 0, 0 < q ≤ 1 and α ≤ p * s − 1. We use variational methods to show the existence and multiplicity of positive solutions of above problem with respect to parameter λ.

Multiplicity and Hölder regularity of solutions for a nonlocal elliptic PDE involving singularity

“…with C N,s , being the normalizing constant. Similar problems to that in (1.3) has been studied by a few authors like Mukherjee & Sreenadh [41], Saoudi [44]. In [41], the authors established the existence of multiple solutions by using the Nehari manifold method.…”

“…Similar problems to that in (1.3) has been studied by a few authors like Mukherjee & Sreenadh [41], Saoudi [44]. In [41], the authors established the existence of multiple solutions by using the Nehari manifold method. In [44], for p = 2 the multiplicity result for the problem (1.3) is proved with the help of the variational method, where the author proved the existence result by converting the nonlocal problem to a local problem.…”

Ground states for a coupled Schrödinger system with general nonlinearities

“…(1.1) reduce to two scalar equations. The Schrödinger equation with different potentials and nonlinearities is actively studied, see for instance [16][17][18][19][20][21]. We just mention some results about asymptotic behaviour of ground state solution.…”

A problem involving a nonlocal operator

“…. For further detail on the embedding results, we refer the reader to [21], [24] and the references there in. We define an associated energy functional to the problem P 1 as…”