Multiplicity Results for the Fractional Laplacian in Expanding Domains

Fractional Laplacian in bounded domains.

The fractional Laplacian operator -(-delta)(alpha/2) appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely, hopping ...

Multiplicity Results of Positive Radial Solutions for p-Laplacian Problems in Exterior Domains

Fractional Laplacian: Pohozaev Identity and Nonexistence Results

In this note we present the Pohozaev identity for the fractional Laplacian. As a consequence of this identity, we prove the nonexistence of nontrivial bounded solutions to semilinear problems with supercritical nonlinearities in starshaped domains. Résumé. Dans cette note, nous présentons l’identité de Pohozaev pour le Laplacien fractionnaire. Comme conséquence de cette identité, nous prouvons ...

Multiplicity Results for Nonlinear Eigenvalue Problems on Unbounded Domains

In this paper we prove a multiplicity result for a class of eigenvalue problems with nonlinear boundary conditions on an unbounded domain. Many results have been obtained by Cârstea and Rădulescu [3], Chabrowski [5], [6], Kandilakis and Lyberopoulos [10], Lisei, Varga and Horváth [13] and Pflüger [16]. MSC 2000. 35J60, 35P30, 58E05.

Multiplicity of Solutions for Non-local Elliptic Equations Driven by Fractional Laplacian

A. We consider the semi-linear elliptic PDEs driven by the fractional Laplacian: { (−∆)su = f (x, u), in Ω, u = 0, in Rn\Ω. By the Mountain Pass Theorem and some other nonlinear analysis methods, the existence and multiplicity of non-trivial solutions for the above equation are established. The validity of the Palais-Smale condition without AmbrosettiRabinowitz condition for non-local el...