다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Progress in Nonlinear Differential Equations and their Applications

The Schrödinger–Poisson equation under the effect of a nonlinear local term

In this paper, we study the problem \[ \left\{\begin{array}{@{}l} -\Delta u + u + V(x)u = u^p,\\[3pt] -\Delta V = \lambda u^2, \quad \displaystyle\lim_{|x| \to +\infty} V(x)=0, \end{array}\right. \] where u, V : ℝ3 → ℝ are radial functions, λ > 0 and 1 < p < 5. We give multiplicity results, depending on p and on the parameter λ.

Multiple bound states for the Schroedinger-Poisson problem

Ground state solutions for the nonlinear Schrödinger–Maxwell equations

This paper is motivated by the study of a version of the so-called Schrodinger–Poisson–Slater problem: 

$$- \Delta u + \omega u + \lambda \left( u^2 \star \frac{1}{|x|} \right) u=|u|^{p-2}u,$$

where ${u \in H^{1}(\mathbb {R}^3)}$. 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, which could be useful in other frameworks. The radial and nonradial cases turn out to yield essentially different situations.

On the Schrödinger–Poisson–Slater System: Behavior of Minimizers, Radial and Nonradial Cases

A priori estimates and existence of positive solutions for strongly nonlinear problems

In this paper we study a coupled nonlinear Schrodinger–Maxwell system of equations. In this framework, we are concerned with the existence of semiclassical states. We use a perturbation scheme in a variational setting in order to study the concentration of the solutions when the Planck constant is supposed to be small enough.

David Ruiz

Papers

The Schrödinger–Poisson equation under the effect of a nonlinear local term

Multiple bound states for the Schroedinger-Poisson problem

On the Schrödinger–Poisson–Slater System: Behavior of Minimizers, Radial and Nonradial Cases

A priori estimates and existence of positive solutions for strongly nonlinear problems

Semiclassical states for coupled schrödinger–maxwell equations: concentration around a sphere