Higher nonlocal problems with bounded potential

Abstract

The aim of this paper is to study a class of nonlocal fractional Laplacian equations depending on two real parameters. More precisely, by using an appropriate analytical context on fractional Sobolev spaces due to Servadei and Valdinoci, we establish the existence of three weak solutions for nonlocal fractional problems exploiting an abstract critical point result for smooth functionals. We emphasize that the dependence of the underlying equation from one of the real parameter is not necessarily of affine type.

References in corpus (1)

• A multiplicity result for nonlocal problems involving nonlinearities with bounded primitive

Cited by in corpus (7)

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• Ground State Solutions of Kirchhoff-type Fractional Dirichlet Problem with $p$-Laplacian
• Existence and Multiplicity of Nontrivial Weak Solutions for Kirchhoff-type Fractional $p$-Laplacian Equation
• Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity