Related papers: The NLS ground states on product spaces
In this paper we prove that ground states of the NLS which satisfy the sufficient conditions for orbital stability of M.Weinstein, are also asymptotically stable, for seemingly generic equations. Here we assume that the NLS has a smooth…
We show the existence and stability of ground state solutions (g.s.s.) for $L^2$-critical magnetic nonlinear Schr\"odinger equations (mNLS) for a class of unbounded electromagnetic potentials. We then give non-existence result by…
We investigate the existence of ground states for the nonlinear Schr\"odinger Equation on star graphs with two subcritical focusing nonlinear terms: a standard power nonlinearity, and a delta-type nonlinearity located at the vertex. We find…
We focus on the study of the stability properties of ground-states for the system of $M$ coupled semilinear Schr\"odinger equations with power-type nonlinearities and couplings. Our results are generalizations of the theory for the single…
We study the focusing mass-subcritical biharmonic nonlinear Schr\"odinger equation (BNLS) on the product space $\mathbb{R}_x^d\times\mathbb{T}_y^n$. Following the crucial scaling arguments introduced in \cite{TTVproduct2014} we establish…
We study existence and properties of ground states for the nonlinear Schr\"odinger equation with combined power nonlinearities \[ -\Delta u= \lambda u + \mu |u|^{q-2} u + |u|^{p-2} u \qquad \text{in $\mathbb{R}^N$, $N \ge 1$,} \] having…
We investigate the existence of ground states with fixed mass for the nonlinear Schr\"odinger equation with a pure power nonlinearity on periodic metric graphs. Within a variational framework, both the $L^2$-subcritical and critical regimes…
We study the existence, the nonexistence, and the shape of the ground states of a Nonlinear Schr\"odinger Equation on a manifold called hybrid plane, that consists of a half-line whose origin is connected to a plane. The nonlinearity is of…
In this paper we consider the logarithmic Schr\"{o}dinger equation on a star graph. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. Then we show the…
In this paper we consider the nonlinear fractional logarithmic Schr\"{o}dinger equation. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. We also prove…
We investigate the existence and the properties of normalized ground states of a nonlinear Schr\"odinger equation on a quantum hybrid formed by two planes connected at a point. The nonlinearities are of power type and $L^2$-subcritical,…
We study the nonlinear Schr\"odinger equation posed on product spaces $\mathbf R^n\times \mathcal M^k$, for $n\geq 1$ and $k\geq1$, with $\mathcal M^k$ any $k$-dimensional compact Riemaniann manifold. The main results concern global…
In this paper, we systematically investigate the ground state solutions of a class of (2,q)-Laplacian Schr\"odinger equations with inhomogeneous nonlinearity. By analyzing global and local constrained variational problems, we establish the…
We prove the existence of ground state solutions for a class of nonlinear elliptic equations, arising in the production of standing wave solutions to an associated family of nonlinear Schr\"odinger equations. We examine two constrained…
We extend to a specific class of systems of nonlinear Schr\"odinger equations (NLS) the theory of asymptotic stability of ground states already proved for the scalar NLS. Here the key point is the choice of an adequate system of modulation…
We review and extend several recent results on the existence of the ground state for the nonlinear Schr\"odinger (NLS) equation on a metric graph. By ground state we mean a minimizer of the NLS energy functional constrained to the manifold…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
We study the existence and the properties of ground states at fixed mass for a focusing nonlinear Schr\"odinger equation in dimension two with a point interaction, an attractive Coulomb potential and a nonlinearity of power type. We prove…
We study the dynamics of solutions of nonlinear Schr\"odinger equation near unstable ground states. The existence of the local center stable manifold around ground states and the asymptotic stability for the solutions on the manifold is…
We consider a nonlinear Schr\"odinger equation (NLS) posed on a graph or network composed of a generic compact part to which a finite number of half-lines are attached. We call this structure a starlike graph. At the vertices of the graph…