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David Ruiz

Publications and source records attributed to David Ruiz.

41 records · Page 3Linked to original sources
arXiv2009

Existence of ground states for a modified nonlinear Schrodinger equation

In this paper we prove existence of ground state solutions of the modified nonlinear Schrodinger equation: $$ -Δu+V(x)u-{1/2}u Δu^{2}=|u|^{p-1}u, x \in \R^N, N \geq 3, $$ under some hypotheses on $V(x)$. This model has been proposed in the theory of superfluid films in plasma physics. As a main novelty with respect to some previous results, we are able to deal with exponents $p\in(1,3)$. The proof is accomplished by minimization under a convenient constraint.

math.AP↗
arXiv2009

Positive and sign-changing clusters around saddle points of the potential for nonlinear elliptic problems

We study the existence of positive and sign-changing multipeak solutions for the stationary Nonlinear Schroedinger Equation. Here no symmetry on $V$ is assumed. It is known that this equation has positive multipeak solutions with all peaks approaching a local maximum of the potential. It is also proved that solutions alternating positive and negative spikes exist in the case of a minima. The aim of this paper is to show the existence of both positive and sign-changing multipeak solutions around a nondegenerate saddle point of the external potential.

math.AP↗
arXiv2009

Ground and bound states for a static Schrodinger-Poisson-Slater problem

In this paper the following version of the Schrodinger-Poisson-Slater problem is studied: $$ - Δu + (u^2 \star \frac{1}{|4πx|}) u=μ|u|^{p-1}u, $$ where $u: \R^3 \to \R$ and $μ>0$. The case $p <2$ being already studied, we consider here $p \geq 2$. For $p>2$ we study both the existence of ground and bound states. It turns out that $p=2$ is critical in a certain sense, and will be studied separately. Finally, we prove that radial solutions satisfy a point-wise exponential decay at infinity for $p>2$.

math.AP↗
arXiv2009

On the Schrodinger-Poisson-Slater system: behavior of minimizers, radial and nonradial cases

This paper is motivated by the study of a version of the so-called Schrodinger-Poisson-Slater problem: $$ - Δu + ωu + λ(u^2 \star \frac{1}{|x|}) u=|u|^{p-2}u,$$ where $u \in H^1(\R^3)$. We are concerned mostly with $p \in (2,3)$. The behavior of radial minimizers motivates the study of the static case $ω=0$. Among other things, we obtain a general lower bound for the Coulomb energy, that could be useful in other frameworks. The radial and nonradial cases turn out to yield essentially different situations.

math.AP↗