Related papers: Trapping by repulsion: the NLS with a delta-prime
We look for ground state solutions to the Schr\"odinger-type system \[ \begin{cases} -\Delta u_j + \lambda_j u_j = \partial_jF(u)\\ \int_{\rn} u_j^2 \, dx = a_j^2\\ (\lambda_j,u_j) \in \mathbb{R} \times H^1(\mathbb{R}^N) \end{cases} j \in…
We study the following doubly critical Schr\"{o}dinger system $$-\Delta u -\frac{\la_1}{|x|^2}u=u^{2^\ast-1}+ \nu \al u^{\al-1}v^\bb, \quad x\in \RN, -\Delta v -\frac{\la_2}{|x|^2}v=v^{2^\ast-1} + \nu \bb u^{\al}v^{\bb-1}, \quad x\in \RN,…
In this article, we study the standing-wave solutions to a class of systems of nonlinear Schr\"odinger equations. Our target is all the standard forms of the NLS systems, with two unknowns, that have a common linear part and cubic…
We focus on the study of ground-states for the system of $M$ coupled semilinear Schr\"odinger equations with power-type nonlinearities and couplings. General results regarding existence and characterization are derived using a variational…
We establish the scattering of solutions to the focusing mass supercritical nonlinear Schr\"odinger equation with a repulsive Dirac delta potential \[ i\partial_{t}u+\partial^{2}_{x}u+\gamma\delta(x)u+|u|^{p-1}u=0, \quad (t,x)\in {\mathbb…
We consider the stationary semilinear Schr\"odinger equation $-\Delta u + a(x) u = f(x,u)$, $u\in H^1(\R^N)$, where $a$ and $f$ are continuous functions converging to some limits $a_\infty>0$ and $f_\infty=f_\infty(u)$ as $|x|\to\infty$. In…
Exact positive and negative energy solutions for the eigenvalue problem of the Schr\"{o}dinger equation in one dimension with a $\delta^\prime$ interaction are found and analyzed. An infinite series of transparency resonance levels in the…
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 consider a Nonlinear Schr\"odinger Equation with a very general non linear term and with a trapping $\delta $ potential on the line. We then discuss the asymptotic behavior of all its small solutions, generalizing a recent result by…
We study dynamics of the 4$d$ energy-critical nonlinear Schr\"odinger equation at the ground state energy. Previously, Duyckaerts and Merle [Geom. Funct. Anal. (2009)] proved that any radial solution with kinetic energy less than that of…
We study the focusing NLS equation in $\mathbb{R}^N$ in the mass-supercritical and energy-subcritical (or intercritical) regime, with $H^1$ data at the mass-energy threshold $ \mathcal{ME}(u_0)=\mathcal{ME}(Q)$, where $Q$ is the ground…
In this paper we are concerned with the fractional Schr\"{o}dinger equation $(-\Delta)^{\alpha} u+V(x)u =f(x, u)$, $x\in \rn$, where $f$ is superlinear, subcritical growth and $u\mapsto\frac{f(x, u)}{\vert u\vert}$ is nondecreasing. When…
We show the existence of ground state solutions to the following stationary system coming from some coupled fractional dispersive equations such as: nonlinear fractional Schr\"odinger (NLFS) equations (for dimension $n=1,\, 2,\, 3$) or NLFS…
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 investigate the existence of ground states at prescribed mass on general metric graphs with half-lines for focusing doubly nonlinear Schr\"odinger equations involving both a standard power nonlinearity and delta nonlinearities located at…
We investigate the existence of normalized ground states for Schr\"odinger equations on noncompact metric graphs in presence of nonlinear point defects, described by nonlinear $\delta$-interactions at some of the vertices of the graph. For…
We consider a dispersive equation of Schr{\"o}dinger type with a non-linearity slightly larger than cubic by a logarithmic factor. This equation is supposed to be an effective model for stable two dimensional quantum droplets with LHY…
From the mathematical side, nonlinear Schr\"odinger equations are usually investigated via variational methods, that cease to work in higher dimensions. This thesis tries to overcome this problem by focusing on spherically symmetric…
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…
This paper concerns the existence of positive ground state solutions for generalized quasilinear Schr\"odinger equations in $\mathbb{R}^N$ with critical growth which arise from plasma physics, as well as high-power ultrashort laser in…