Asymptotically linear Schrödinger-Poisson systems with potentials vanishing at infinity

In this paper, we are concerned with the following nonlinear Schrödinger-Poisson equations

(P)     

The Schrödinger-Poisson equation under the effect of a nonlinear local term

In this paper we study the problem

     

Positive solutions for some non-autonomous Schrödinger-Poisson systems

In this paper we study the Schrödinger-Poisson system

(SP)     

Existence and multiplicity results for the nonlinear Schrödinger-Poisson systems

In this paper, we study the existence and multiplicity results for the nonlinear Schrödinger-Poisson systems

(∗)     

Large time WKB approximation for multi-dimensional semiclassical Schrödinger-Poisson system

We consider the semiclassical Schrödinger-Poisson system with a special initial data of WKB type such that the solution of the limiting hydrodynamical equation becomes time-global in dimensions at least three. We give an example of such initial data in the focusing case via the analysis of the compressible Euler-Poisson equations. This example is a large data with radial symmetry, and is beyond the reach of the previous results because the phase part decays too slowly. Extending previous results in this direction, we justify the WKB approximation of the solution with this data for an arbitrarily large interval of R₊.     

Concentration and compactness in nonlinear Schrödinger-Poisson system with a general nonlinearity

In this paper we use a concentration and compactness argument to prove the existence of a nontrivial non-radial solution to the nonlinear Schrödinger-Poisson equations in R³, assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions.     

Ground state solutions for the nonlinear Schrödinger-Maxwell equations

In this paper we study the nonlinear Schrödinger-Maxwell equations

     

On the existence of solutions for the Schrödinger-Poisson equations

In this paper, we are concerned with the system of Schrödinger-Poisson equations

(*)     

Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials

We establish the existence and multiplicity of semiclassical bound states of the following nonlinear Schrödinger equation:

     

Existence of solutions for non-periodic superlinear Schrödinger equations without (AR) condition

The existence of solutions is obtained for a class of the non-periodic Schrödinger equation −Δu + V(x)u = f(x, u), x ∈ R^N, by the generalized mountain pass theorem, where V is large at infinity and f is superlinear as |u| → ∞.     

Quasi-periodic solutions of nonlinear Schrödinger equations of higher dimension

It is shown that there are plenty of quasi-periodic solutions of nonlinear Schrödinger equations of higher spatial dimension, where the dimension of the frequency vectors of the quasi-periodic solutions are equal to that of the space.     

Stability and instability of standing waves to a system of Schrödinger equations with combined power-type nonlinearities

We obtain the existence of standing wave solutions to a coupled nonlinear Schrödinger system

     

Periodic solutions for Hamiltonian systems without Ambrosetti-Rabinowitz condition and spectrum 0

In this paper, we consider the superquadratic second order Hamiltonian system

     

On the location and profile of spike-layer nodal solutions to nonlinear Schrödinger equations

The existence and concentration behavior of a nodal solution are established for the equation

     

Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions

In [T. Duyckaerts, F. Merle, Dynamic of threshold solutions for energy-critical NLS, preprint, arXiv:0710.5915 [math.AP]], T. Duyckaerts and F. Merle studied the variational structure near the ground state solution W of the energy critical NLS and classified the solutions with the threshold energy E(W) in dimensions d=3,4,5 under the radial assumption. In this paper, we extend the results to all dimensions d?6. The main issue in high dimensions is the non-Lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of W.     

Multiple positive solutions for a Schrödinger-Poisson-Slater system

In this paper we investigate the existence of positive solutions to the following Schrödinger-Poisson-Slater system

     

Instability of standing waves for a class of nonlinear Schrödinger equations

This paper discusses a class of nonlinear Schrödinger equations with different power nonlinearities. We first establish the existence of standing wave associated with the ground states by variational calculus. Then by the potential well argument and the concavity method, we get a sharp condition for blowup and global existence to the solutions of the Cauchy problem and answer such a problem: how small are the initial data, the global solutions exist? At last we prove the instability of standing wave by combing those results.