Szczegóły publikacji
Opis bibliograficzny
Existence results for Kirchhoff-type superlinear problems involving the fractional Laplacian / Zhang Binlin, Vicenţiu D. RǍDULESCU, Li Wang // Proceedings of the Royal Society of Edinburgh Section. A-Mathematics ; ISSN 0308-2105. — 2019 — vol. 149, s. 1061–1081. — Bibliogr. s. 1079–1081. — V. D. Rǎdulescu – dod. afiliacja: Romanian Academy
Autorzy (3)
- Binlin Zhang
- AGHRǎdulescu Vicenţiu
- Wang Li
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 124634 |
|---|---|
| Data dodania do BaDAP | 2019-10-08 |
| DOI | 10.1017/prm.2018.105 |
| Rok publikacji | 2019 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Proceedings of the Royal Society of Edinburgh Section, A, Mathematics |
Abstract
In this paper, we study the existence and multiplicity of solutions for Kirchhoff-type superlinear problems involving non-local integro-differential operators. As a particular case, we consider the following Kirchhoff-type fractional Laplace equation:.{M(integral integral(R2N) vertical bar u(x) -u(y)vertical bar(2)/vertical bar x-y vertical bar(N vertical bar 2s) dxdy) (-Delta)(s)u = f(x,u) in Omega, , where (-.)s is the fractional Laplace operator, s. (0, 1), N > 2s, O is an open bounded subset of RN with smooth boundary.O, M : R+ 0. R+ is a continuous function satisfying certain assumptions, and f(x, u) is superlinear at infinity. By computing the critical groups at zero and at infinity, we obtain the existence of non-trivial solutions for the above problem via Morse theory. To the best of our knowledge, our results are new in the study of Kirchhoff-type Laplacian problems.
