Related papers: NLS ground states on the half-line with point inte…
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 NLS Equation on the line with a point interaction given by the superposition of an attractive delta potential with a dipole interaction, in the cases of $L^2$-subcritical and $L^2$-critical nonlinearity. For a subcritical…
We investigate the problem of existence and uniqueness of ground states at fixed mass for two families of focusing nonlinear Schr\"odinger equations on the line. The first family consists of NLS with power nonlinearities concentrated at a…
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…
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 investigate the existence of ground states with prescribed mass for the NLS energy with combined $L^2$-critical and subcritical nonlinearities, on a general non-compact metric graph $\mathcal{G}$. The interplay between the different…
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 study the ground states for the Schr\"odinger equation with a focusing nonlinearity and a point interaction in dimension three. We establish that ground states exist for every value of the mass; moreover they are positive, radially…
In this paper, we establish the existence of bounded states and geometrically distinct solutions for the subcritical NLS equation with attractive potential on metric graphs $\mathcal{G}$ when the mass $\mu$ is large enough.We show that the…
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 consider the subcritical nonlinear Schr\"odinger equation on non-compact quantum graphs with an attractive potential supported in the compact core, and investigate the existence and the nonexistence of Ground States, defined as…
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 determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called…
We study the existence of bound and ground states for a class of nonlinear elliptic systems in $\mathbb{R}^N$. These equations involve critical power nonlinearities and Hardy-type singular potentials, coupled by a term containing up to…
We establish the existence and provide explicit expressions for the stationary states of the one-dimensional Schr\"odinger equation with a repulsive delta-prime potential and a focusing nonlinearity of power type. Furthermore, we prove…
We establish general non-uniqueness results for normalized ground states of nonlinear Schr\"odinger equations with power nonlinearity on metric graphs. Basically, we show that, whenever in the $L^2$-subcritical regime a graph hosts ground…
We investigate the existence of ground states of prescribed mass, for the nonlinear Schroedinger energy on a noncompact metric graph G. While in some cases the topology of G may rule out or, on the contrary, guarantee the existence of…
We consider ground states of a pseudo-relativistic Fermi system in the $L^2$-critical case. We prove that the system admits ground states, if and only if the attractive strength $a$ satisfies $0<a<D_{4/3,2}$, where $D_{4/3,2}\in(0, \infty)$…
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 consider the problem of uniqueness of ground states of prescribed mass for the Nonlinear Schr\"odinger Energy with power nonlinearity on noncompact metric graphs. We first establish that the Lagrange multiplier appearing in the NLS…