Infinitely many positive solutions for Schrödinger-poisson systems with nonsymmetry potentials

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

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.

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

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + u + λφu = µf(u) +|u|p−2|u|, x ∈R3 (−∆t)φ = u2, x ∈R3 where λ,µ are two parameters, s,t ∈ (0,1] ,2t + 4s > 3 ,1 < p ≤ 2∗ s and f : R → R is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with ...

Infinitely Many Positive Solutions for Nonlinear Equations with Non-symmetric Potentials

We consider the following nonlinear Schrödinger equation { ∆u− (1 + δV )u + f(u) = 0 in R , u > 0 in R , u ∈ H(R ) where V is a continuous potential and f(u) is a nonlinearity satisfying some decay condition and some non-degeneracy condition, respectively. Using localized energy method, we prove that there exists a δ0 such that for 0 < δ < δ0, the above problem has infinitely many positive solu...

Infinitely Many Solutions for Fractional Schrödinger-poisson Systems with Sign-changing Potential

In this article, we prove the existence of multiple solutions for following fractional Schrödinger-Poisson system with sign-changing potential (−∆)u+ V (x)u+ λφu = f(x, u), x ∈ R, (−∆)φ = u, x ∈ R, where (−∆)α denotes the fractional Laplacian of order α ∈ (0, 1), and the potential V is allowed to be sign-changing. Under certain assumptions on f , we obtain infinitely many solutions for this sys...