相关论文: Existence and nonrelativistic limit of ground stat…

We investigate the existence and stability of ground states for the defocusing nonlinear Schr\"odinger equation on non-compact metric graphs. We establish a sharp criterion for the existence of action ground states in terms of the spectral…

We investigate the action ground states of the defocusing nonlinear Schr\"odinger equation with and without rotation. Our primary focus is on characterizing the relationship between the action ground states and the energy ground states.…

In this paper, we investigate the nonrelativistic limit of normalized solutions to a nonlinear Dirac equation as given below: \begin{equation*} \begin{cases} &-i c\sum\limits_{k=1}^3\alpha_k\partial_k u +mc^2 \beta {u}- \Gamma * (K…

In this paper, we study the asymptotic behavior of energy and action ground states to the following pseudo-relativistic Hartree equation \[ \left(\sqrt{-c^2\Delta +m^2c^4}-mc^2\right)u + \lambda u = \left(|x|^{-1}*|u|^2\right)u \] as the…

In this work we study the existence of ground-state solutions of Dirac equations with potentials which are allowed to vanish at infinity. The approach is based on minimization of the energy functional over a generalized Nehari set. Some…

We study analytically the existence and uniqueness of the ground state of the nonlinear Schr\"{o}dinger equation (NLSE) with a general power nonlinearity described by the power index $\sigma\ge0$. For the NLSE under a box or a harmonic…

We investigate the ground states of the one-dimensional nonlinear Schr\"odinger equation with a defect located at a fixed point. The nonlinearity is focusing and consists of a subcritical power. The notion of ground state can be defined in…

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 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 consider the nonlinear Schr\''odinger equation on a strip with Neumann boundary conditions and a delta condition on the $x$-axis. First, we show the existence of ground states as minimizers of the action or of the energy under suitable…

We study the existence of solutions of the following nonlinear Schr\"odinger equation \begin{equation*} -\Delta u + \Big(V(x)-\frac{\mu}{|x|^2}\Big) u = f(x,u) \hbox{ for } x\in\mathbb{R}^N\setminus\{0\}, \end{equation*} where…

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 investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that…

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…

The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…

We investigate the ground states for the focusing, subcritical nonlinear Schr\"odinger equation with a point defect in dimension two, defined as the minimizers of the energy functional at fixed mass. We prove that ground states exist for…

We demonstrate existence of positive bound and ground states for a system of coupled nonlinear Schr\"odinger--Korteweg-de Vries equations. More precisely, we prove there is a positive radially symmetric ground state if either the coupling…

In this paper we prove existence of ground state solutions of the modified nonlinear Schrodinger equation: $$ -\Delta u+V(x)u-{1/2}u \Delta u^{2}=|u|^{p-1}u, x \in \R^N, N \geq 3, $$ under some hypotheses on $V(x)$. This model has been…

We consider the existence of bound and ground states for a family of nonlinear elliptic systems in $\mathbb{R}^N$, which involves equations with critical power nonlinearities and Hardy-type singular potentials. The equations are coupled by…

We study the existence of ground and bound state solutions for a system of coupled Schr\"odinger equations with linear and nonlinear couplings in $\mathbb{R}^N$. By studying the limit system and using concentration compactness arguments, we…