Solutions for a Kirchhoff equation with critical Caffarelli–Kohn–Nirenberg growth and discontinuous nonlinearity

Santos, Gelson G. dos; Figueiredo, Giovany M.

doi:10.1007/s00033-018-0966-1

Cited by 7 publications

(2 citation statements)

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“…where g can have discontinuities. 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: 78%

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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: 78%

“…(3.1) We provide some properties of the functionals I µ and I α in the following lemma and these results can be proved by following the arguments of Lemma 3.1 of [16].…”

Section: Existence Results Formentioning

confidence: 99%