Related papers: Normalized solutions for nonlinear Schr\"odinger e…
This paper is devoted to the existence of multiple sign-changing solutions of prescribed mass for a mass-supercritical nonlinear Schr\"odinger equation set on a compact metric graph. In particular, we obtain, in the supercritical mass…
We look for solutions to the Schr\"odinger equation \[ -\Delta u + \lambda u = g(u) \quad \text{in } \mathbb{R}^N \] coupled with the mass constraint $\int_{\mathbb{R}^N}|u|^2\,dx = \rho^2$, with $N\ge2$. The behaviour of $g$ at the origin…
We prove global existence and stability of solution to the mass-critical stochastic nonlinear Schr\"odinger equation in $d=1$ at $L^2$ regularity. Our construction starts with the existence of solution to the truncated subcritical problem.…
We analyze $L^2$-normalized solutions of nonlinear Schr\"odinger systems of Gross-Pitaevskii type, on bounded domains, with homogeneous Dirichlet boundary conditions. We provide sufficient conditions for the existence of orbitally stable…
This paper investigates the existence of normalized solutions for the following Chern-Simons-Schr\"odinger equation: \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+\lambda u+\left(\frac{h^{2}(\vert x\vert)}{\vert…
We study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schr\"odinger equation of the form \begin{equation*} -\Delta u+\lambda u=g(u), \quad u \in H^1(\mathbb{R}^N), \, N \geq 1. \end{equation*} Our…
The purpose of this paper is to prove some results on the absence of bound states for certain nonlinear Schr\"odinger equations on noncompact metric graphs with localized nonlinearity. In particular, we show how the topological and metric…
In this paper, we consider solutions to the following nonlinear Schr\"odinger equation with competing Hartree-type nonlinearities, $$ -\Delta u + \lambda u=\left(|x|^{-\gamma_1} \ast |u|^2\right) u - \left(|x|^{-\gamma_2} \ast |u|^2\right)…
In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to…
We consider the existence of \emph{normalized} solutions in $H^1(\R^N) \times H^1(\R^N)$ for systems of nonlinear Schr\"odinger equations which appear in models for binary mixtures of ultracold quantum gases. Making a solitary wave ansatz…
We investigate normalized solutions for doubly nonlinear Schr\"odinger equations on the real line with a defocusing standard nonlinearity and a focusing nonlinear point interaction of $\delta$-type at the origin. We provide a complete…
We investigate the existence and the singular limit of normalized ground states for focusing doubly nonlinear Schr\"odinger equations with both standard and concentrated nonlinearities on two-dimensional square grids. First, we provide…
We are concerned with solutions of the following quasilinear Schr\"odinger equations \begin{eqnarray*} -{\mathrm{div}}\left(\varphi^{2}(u) \nabla u\right)+\varphi(u) \varphi^{\prime}(u)|\nabla u|^{2}+\lambda u=f(u), \quad x \in…
This paper is concerned with the existence of normalized solutions of the nonlinear Schr\"odinger equation \[ -\Delta u+V(x)u+\lambda u = |u|^{p-2}u \qquad\text{in $\mathbb{R}^N$} \] in the mass supercritical and Sobolev subcritical case…
We consider the Schroedinger equation with a subcritical focusing power nonlinearity on a noncompact metric graph, and prove that for every finite edge there exists a threshold value of the mass, beyond which there exists a positive bound…
We develop a new approach to the investigation of normalized solutions for nonlinear Schr\"odinger equations based on the analysis of the masses of ground states of the corresponding action functional. Our first result is a complete…
In this paper, using a discrete Schwarz rearrangement on lattice graphs developed in \cite{DSR}, we study the existence of global minimizers for the following functional $I:H^1\left(\mathbb{Z}^N\right)\to \R$, $$I(u)=\frac{1}{2}…
We study the defocusing nonlinear Schr\"odinger equation on noncompact metric graphs under general self-adjoint vertex conditions ensuring the existence of a negative eigenvalue of the Hamiltonian operator. First, we focus on the existence…
In this paper, we investigate the following nonlinear Schr\"odinger equation with Neumann boundary conditions: \begin{equation*} \begin{cases} -\Delta u+ \lambda u= f(u) & {\rm in} \,~ \Omega,\\ \displaystyle\frac{\partial u}{\partial…
We consider the nonlinear Schr\"odinger equation with focusing power-type nonlinearity on compact graphs with at least one terminal edge, i.e. an edge ending with a vertex of degree 1. On the one hand, we introduce the associated action…