Related papers: Fractional Schrodinger-Poisson Equations With Gene…
This paper is concerned with a nonlinear fractional Sch\"ordinger system in $\mathbb{{R}}$ with intraspecies interactions $a_{i}>0 \ (i=1,2)$ and interspecies interactions $\beta \in\mathbb{{R}}$. We study this system by solving an…
Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…
We present a general strategy to solve the stationary Schr\"odinger-Poisson (SP) system of equations for multistates with axial symmetry. The approach allows us to obtain the well known single and multistate solutions with spherical…
Recently it was pointed out that the solutions found in literature for the space fractional Schr\"odinger equation in a piecewise manner are wrong, except the case with the delta potential. We reanalyze this problem and show that an exact…
This paper is concerned with the existence and qualitative properties of positive ground state solutions for the planar Schr\"odinger-Newton equation on the disc. First, we prove the existence and radial symmetry of all the positive ground…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
We deal with the following fractional Schr\"odinger-Poisson equation with magnetic field \begin{equation} \varepsilon^{2s}(-\Delta)_{A/\varepsilon}^{s}u+V(x)u+\varepsilon^{-2t}(|x|^{2t-3}*|u|^{2})u=f(|u|^{2})u+|u|^{2^{*}_{s}-2}u \quad…
For a certain class of solutions of the cubic nonlinear Sch\"odinger equation we prove non-existence in the generic case. In the nongeneric case we present a two-parameter set of solutions, bounded or unbounded, depending on corresponding…
In this paper, the space-fractional Schr\"{o}dinger equations with singular potentials are studied. Delta-like or even higher-order singularities are allowed. By using the regularising techniques, we introduce a family of 'weakened'…
We exhibit existence of non-trivial solutions of some fractional linear Schr\"odinger equations which are radial and vanish at the origin. This is in stark contrast to what happens in the local case. We also prove analogous results in the…
In this article, we study the standing-wave solutions to a class of systems of nonlinear Schr\"odinger equations. Our target is all the standard forms of the NLS systems, with two unknowns, that have a common linear part and cubic…
This paper is dedicated to studying the nonlinear Schr\"odinger equations of the form \begin{equation*}\label{KE} \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(u), & x\in \R^N; u\in H^1(\R^N), \end{array} \right. \end{equation*} where…
A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…
All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the…
In this paper, we address the existence of ground state solutions for Schrodinger equations in the presence of local and nonlocal operators and two critical nonlinearities associated with each operator. The situation is completely solved in…
In this work, we study the existence of various classes of standing waves for a nonlinear Schr\"odinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state…
We investigate the following inhomogeneous nonlinear Schr\"odinger equation in the radial regime, featuring a focusing energy-critical nonlinearity and a defocusing perturbation: $$ i\partial_t u +\Delta u =|x|^{-a} |u|^{p-2} u - |x|^{-b}…
The algorithm for generation of exact solutions of the nonlinear equation in partial derivatives of a divergent type which is included in the formulation of magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary Schr\"odinger…
The semilinear space-time fractional Schr\"odinger equation is considered. First, we give the explicit form for the fundamental solutions by using the Fox $H$-functions in order to to establish some $L^s$ decay estimates. After that, we…
We prove the existence of global analytic solutions to the nonlinear Schr\"odinger equation in one dimension for a certain type of analytic initial data in $L^2$.