ON STRONGLY INDEFINITE SYSTEMS INVOLVING FRACTIONAL ELLIPTIC OPERATORS

Existence Results for Strongly Indefinite Elliptic Systems

In this paper, we show the existence of solutions for the strongly indefinite elliptic system −∆u = λu+ f(x, v) in Ω, −∆v = λv + g(x, u) in Ω, u = v = 0, on ∂Ω, where Ω is a bounded domain in RN (N ≥ 3) with smooth boundary, λk0 < λ < λk0+1, where λk is the kth eigenvalue of −∆ in Ω with zero Dirichlet boundary condition. Both cases when f, g being superlinear and asymptotically linear at infin...

On certain fractional calculus operators involving generalized Mittag-Leffler function

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

On a superquadratic elliptic system with strongly indefinite structure

In this paper, we consider the elliptic system