Related papers: Normalized NLS ground states on a double plane hyb…
In this paper, we consider the existence of normalized solutions for the following biharmonic nonlinear Schr\"{o}dinger system \begin{equation*} \begin{cases} \Delta^2u+\alpha_{1}\Delta u+\lambda u=\beta r_{1}|u|^{r_{1}-2}|v|^{r_{2}} u &…
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…
We investigate the ground state of a system of interacting particles in small nonlinear lattices with M > 2 sites, using as a prototypical example the discrete nonlinear Schroedinger equation that has been recently used extensively in the…
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 of ground states for the focusing nonlinear Schroedinger equation on a prototypical doubly periodic metric graph. When the nonlinearity power is below 4, ground states exist for every value of the mass, while,…
Some focusing coupled Schrodinger equations are investigated. First, existence of ground state is obtained. Second, global and non global existence of solutions are discussed via potential-well method. Finally, strong instability of…
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…
In this paper, we consider the following nonlinear Schr\"{o}dinger equations with mixed nonlinearities: \begin{eqnarray*} \left\{\aligned &-\Delta u=\lambda u+\mu |u|^{q-2}u+|u|^{2^*-2}u\quad\text{in }\mathbb{R}^N,\\ &u\in…
In this paper we study the one-dimensional logarithmic Schr\"odinger equation perturbed by an attractive $\delta^{\prime}$-interaction \[ i\partial_{t}u+\partial^{2}_{x}u+ \gamma\delta^{\prime}(x)u+u\, \mbox{Log}\left|u\right|^{2}=0, \quad…
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 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…
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…
The uniqueness of the positive ground state solutions of fractional Shrodinger equations with a harmonic potential has not been covered by the breakthrough method developed in [1, 2]. It has remained an open question for years. [3] and [5]…
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 study normalized solutions $(\mu,u)\in \mathbb{R} \times H^1(\mathbb{R}^N)$ to nonlinear Schr\"odinger equations $$ -\Delta u + \mu u = g(u)\quad \hbox{in}\ \mathbb{R}^N, \qquad \frac{1}{2}\int_{\mathbb{R}^N} u^2 dx = m, $$ where $N\geq…
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 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…
This paper is concerned with the following logarithmic Schr\"{o}dinger system: $$\left\{\begin{align} \ &\ -\Delta u_1+\omega_1u_1=\mu_1 u_1\log u_1^2+\frac{2p}{p+q}|u_2|^{q}|u_1|^{p-2}u_1,\\ \ &\ -\Delta u_2+\omega_2u_2=\mu_2 u_2\log…
We prove the existence of radial and radially decreasing ground states of an m-coupled nonlinear Schrodinger equation with a general nonlinearity.
We study the existence of ground state standing waves, of prescribed mass, for the nonlinear Schr\"{o}dinger equation with mixed power nonlinearities \begin{equation*} i \partial_t v + \Delta v + \mu v |v|^{q-2} + v |v|^{2^* - 2} = 0, \quad…