Higher nonlocal problems with bounded potential

Abstract

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.

Existence Results for Fractional P-Laplacian Systems via Young Measures

“…The literature on nonlocal operators and their applications is very interesting and large. We refer to [1,10,11,12,13,18,19,20,25] and other references therein.…”

Multiplicity results for the non-homogeneous fractionalp-Kirchhoff equations with concave–convex nonlinearities

“…This type of operators arises in a quite natural way in many different applications, such as continuum mechanics, phase transition phenomena, population dynamics, minimal surfaces and game theory, as they are the typical outcome of stochastically stabilization of Lévy processes (see [5][6][7][8][9] and the references therein). The literature on fractional operators and their applications is very huge, here we just mention a few, see for example [10][11][12][13][14][15][16][17][18][19][20], especially [21] and [22,23] for two different fractional Laplacian involving concave-convex nonlinearities. On the subject of concave-convex nonlinearities involving the classical Laplacian operator, for instance, we refer the reader to [24].…”

Nonlinear equations involving the square root of the Laplacian

“…As pointed out in [11], the fractions of the Laplacian, such as the previous square root of the Laplacian A 1/2 , are the infinitesimal generators of Lévy stable diffusion processes and appear in anomalous diffusions in plasmas, flames propagation and chemical reactions in liquids, population dynamics, geophysical fluid dynamics, and American options in finance. Moreover, a lot of interest has been devoted to elliptic equations involving the fractions of the Laplacian, (see, among others, the papers [1,2,3,5,8,14,24,28,35,40] as well as [7,25,27,30,31,32,34] and the references therein). See also the papers [4,37] for related topics.…”