Existence of non-trivial solutions for fractional Schrödinger-Poisson systems with subcritical growth

On a class of nonlinear fractional Schrödinger-Poisson systems

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...

Existence of three solutions for a class of fractional boundary value systems

In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of t...

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Existence of Solutions to Fractional Hamiltonian Systems with Combined Nonlinearities

This article concerns the existence of solutions for the fractional Hamiltonian system −tD ∞ ` −∞D α t u(t) ́ − L(t)u(t) +∇W (t, u(t)) = 0, u ∈ H(R,R), where α ∈ (1/2, 1), L ∈ C(R,Rn ) is a symmetric and positive definite matrix. The novelty of this article is that if τ1|u| ≤ (L(t)u, u) ≤ τ2|u| and the nonlinearity W (t, u) involves a combination of superquadratic and subquadratic terms, the Ham...

Existence of Entropy Solutions for Nonsymmetric Fractional Systems

The present work focuses on entropy solutions for the fractional Cauchy problem of nonsymmetric systems. We impose sufficient conditions on the parameters to obtain bounded solutions of L∞. The solutions attained are unique and exclusive. Performance is established by utilizing the maximum principle for certain generalized time and space-fractional diffusion equations. The fractional differenti...

Infinitely many radial solutions for the fractional Schrödinger-Poisson systems

In this paper, we study the following fractional Schrödinger-poisson systems involving fractional Laplacian operator { (−∆)su+ V (|x|)u+ φ(|x|, u) = f(|x|, u), x ∈ R3, (−∆)tφ = u2, x ∈ R3, (1) where (−∆)s(s ∈ (0, 1)) and (−∆)t(t ∈ (0, 1)) denotes the fractional Laplacian. By variational methods, we obtain the existence of a sequence of radial solutions. c ©2016 All rights reserved.