The purpose of this paper is to investigate the existence of weak solutions for a Kirchhoff type problem driven by a non-local integro-differential operator of elliptic type with homogeneous Dirichlet boundary conditions as follows:. {M(∫R2N|u(x)-u(y)|pK(x-y)dxdy)LKpu=f(x,u)inΩ,u=0inRNΩ, where LKp is a non-local operator with singular kernel K, Ω is an open bounded subset of RN with Lipshcitz boundary ∂ Ω, M is a continuous function and f is a Carathéodory function satisfying the Ambrosetti-Rabinowitz type condition. We discuss the above-mentioned problem in two cases: when f satisfies sublinear growth condition, the existence of nontrivial weak solutions is obtained by applying the direct method in variational methods; when f satisfies suplinear growth condition, the existence of two nontrivial weak solutions is obtained by using the Mountain Pass
Existence of solutions for Kirchhoff type problem involving thenon-local fractional p-Laplacian / Ferrara, Massimiliano; Zhang, B; Xiang, M. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 424:2(2015), pp. 1021-1041. [10.1016/j.jmaa.2014.11.055]
Existence of solutions for Kirchhoff type problem involving thenon-local fractional p-Laplacian
FERRARA, MassimilianoSupervision
;
2015-01-01
Abstract
The purpose of this paper is to investigate the existence of weak solutions for a Kirchhoff type problem driven by a non-local integro-differential operator of elliptic type with homogeneous Dirichlet boundary conditions as follows:. {M(∫R2N|u(x)-u(y)|pK(x-y)dxdy)LKpu=f(x,u)inΩ,u=0inRNΩ, where LKp is a non-local operator with singular kernel K, Ω is an open bounded subset of RN with Lipshcitz boundary ∂ Ω, M is a continuous function and f is a Carathéodory function satisfying the Ambrosetti-Rabinowitz type condition. We discuss the above-mentioned problem in two cases: when f satisfies sublinear growth condition, the existence of nontrivial weak solutions is obtained by applying the direct method in variational methods; when f satisfies suplinear growth condition, the existence of two nontrivial weak solutions is obtained by using the Mountain PassFile | Dimensione | Formato | |
---|---|---|---|
Ferrara JMAA.pdf
accesso aperto
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
1.11 MB
Formato
Adobe PDF
|
1.11 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.