Szczegóły publikacji
Opis bibliograficzny
Superlinear Schrödinger-Kirchhoff type problems involving the fractional $p$-Laplacian and critical exponent / Mingqi Xiang, Binlin Zhang, Vicenţiu D. RĂDULESCU // Advances in Nonlinear Analysis [Dokument elektroniczny]. — Czasopismo elektroniczne ; ISSN 2191-950X. — 2020 — vol. 9 iss. 1, s. 690–709. — Wymagania systemowe: Adobe Reader. — Bibliogr. s. 707–709, Abstr. — Publikacja dostępna online od: 2019-06-08. — V. D. Rădulescu - dod. afiliacja: University of Craiova, Romania
Autorzy (3)
- Xiang Mingqi
- Zhang Binlin
- AGHRǎdulescu Vicenţiu
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 124899 |
|---|---|
| Data dodania do BaDAP | 2020-01-15 |
| Tekst źródłowy | URL |
| DOI | 10.1515/anona-2020-0021 |
| Rok publikacji | 2020 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Advances in Nonlinear Analysis |
Abstract
This paper concerns the existence and multiplicity of solutions for the Schrodinger-Kirchhoff type problems involving the fractional p-Laplacian and critical exponent. As a particular case, we study the following degenerate Kirchhoff-type nonlocal problem: ||u||λ(θ-1)p[λ(-Delta;)spu+v(x)|u|p-2u]=|u|p∗s-2u+f(x,u)in ℝ ||u||λ=( λff∫ ∫ ℝN|u(x)-u(y)|p/|x-y|N+ps dxdy + ∫ ℝN V(x)jujpdx)1/p where is the fractional p-Laplacian with 0 < s < 1 < p < N/s, ps∗=Np/(N-ps) is the critical fractional Sobolev exponent, λ > 0 is a real parameter, 1<θ≤ps∗/p, and f : ℝN × ℝ → ℝ is a Carathéodory function satisfying superlinear growth conditions. For θϵ(1,ps∗/p), by using the concentration compactness principle in fractional Sobolev spaces, we show that if f(x, t) is odd with respect to t, for any m ϵ N+ there exists a Λm > 0 such that the above problem has m pairs of solutions for all λ ϵ (0, Λm]. For θ=ps∗/p, by using Krasnoselskii's genus theory, we get the existence of infinitely many solutions for the above problem for λ large enough. The main features, as well as the main difficulties, of this paper are the facts that the Kirchhoff function is zero at zero and the potential function satisfies the critical frequency infxϵℝ V(x) = 0. In particular, we also consider that the Kirchhoff term satisfies the critical assumption and the nonlinear term satisfies critical and superlinear growth conditions. To the best of our knowledge, our results are new even in p-Laplacian case. © 2020 Mingqi Xiang et al., published by De Gruyter 2020.
