Existence and behavior of the solutions for an elliptic equation with a nonlocal operator involving critical and discontinuous nonlinearity

Santos, Gelson C. G. dos; Tavares, Leandro S.

doi:10.1016/j.jmaa.2020.124530

Cited by 8 publications

(3 citation statements)

References 22 publications

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“…The authors in [16] and [18] extended the result of [5] for a Kirchhoff type problem involving critical Caffarelli-Kohn-Nirenberg growth and for a Schrödinger-Kirchhoff equation, respectively. Recently, Santos & Tavares in [17] considered the problem…”

Section: Introductionmentioning

confidence: 99%

“…We also cite [1,3,4,7,11,13,14,32,34] and the references therein for readers to have a glimpse of the problems of the type as in (1.1) − (1.3). Inspired by the above works, specifically [5,6,11,12,17] we analyze our problem (P α ). The problem (P α ) with singularity, critical and discontinuous nonlinearities is a new and first work in the literature, at least to our knowledge.…”

Section: Introductionmentioning

confidence: 99%

“…We now provide the notion of weak solution to (P α ) (influenced by [17]). We say a function u ∈ W s,p 0 (Ω) to be a weak solution of (P α ) if u > 0 a.e.…”

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confidence: 99%

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A singular elliptic problem involving fractional $p$-Laplacian and a discontinuous critical nonlinearity

Saoudi,

Panda,

Choudhuri

2021

Preprint

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In this article, we prove the existence of solutions to a nonlinear nonlocal elliptic problem with a singualrity and a discontinuous critical nonlinearity which is given as follows.where Ω ⊂ R N is a bounded domain with Lipschitz boundary, s ∈ (0, 1), 2 < p < N s , γ ∈ (0, 1), λ, µ > 0, α ≥ 0 is real, H is the Heaviside function, i.e. H(a) = 0 if a ≤ 0, H(a) = 1 if a > 0 and p * s = N p N −sp is the fractional critical Sobolev exponent. Under suitable assumptions on the function g, we prove the existence of solution to the problem. Furthermore, we show that as α → 0 + , the sequence of solutions of (0.1) for each such α converges to a solution of the problem for which α = 0.

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Section: Introductionmentioning

confidence: 99%