Small perturbations of critical nonlocal equations with variable exponents

• Autorzy: Tao Lulu , He Rui , Liang Sihua

Identyfikatory

DOI

10.1515/dema-2023-0266

• Języki publikacji: EN

Abstrakty

EN

In this article, we are concerned with the following critical nonlocal equation with variable exponents: [wzór], where Ω⊂RN is a bounded domain with Lipschitz boundary, N ≥ 2 , p ∈ C (Ω×Ω) is symmetric, f : C(Ω×R)→R is a continuous function, and λ is a real positive parameter. We also assume [wzór] is the critical Sobolev exponent for variable exponents. We prove the existence of non-trivial solutions in the case of low perturbations (λ small enough) by using the mountain pass theorem, the concentration-compactness principles for fractional Sobolev spaces with variable exponents, and the Moser iteration method. The features of this article are the following: (1) the function f does not satisfy the usual Ambrosetti-Rabinowitz condition and (2) this article contains the presence of critical terms, which can be viewed as a partial extension of the previous results concerning the the existence of solutions to this problem in the case of s = 1 and subcritical case.

Słowa kluczowe

EN

fractional p-Laplace operator; p(.)-Laplacian; critical nonlinearity; Moser iteration; concentration-compactness principles; variational methods

PL

operator ułamkowy p-Laplace'a; iteracja Mosera; metody wariacyjne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20230266
• Opis fizyczny: Bibliogr. 43 poz.

Twórcy

autor

Tao Lulu

• College of Mathematics, Changchun Normal University, Changchun 130032, Jilin, PR China

autor

He Rui

• College of Mathematics, Changchun Normal University, Changchun 130032, Jilin, PR China

autor

Liang Sihua

• College of Mathematics, Changchun Normal University, Changchun 130032, Jilin, PR China

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).