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

By D. Ruiz. 2009

207 citations recorded by the source corpus.

AbstractThis paper is motivated by the study of a version of the so-called Schrödinger–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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6a3383f6b15ba544a39ed0286304e79ca9d7c666

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Infinitely many sign-changing solutions for the nonlinear Schrödinger–Poisson system (2014, background): “In [27], Ruiz studied the profile of the radial ground state solutions to (1.”
Existence and instability of standing waves with prescribed norm for a class of Schrödinger–Poisson equations (2011, background): “Indeed, u ∈ L(R(3)) for all q ∈ [3, 6], see [32], and from (7.”
Existence and asymptotic behavior of sign-changing solutions for the nonlinear Schrödinger–Poisson system in $${\mathbb{R}^3}$$R3 (2015, background): “1), especially on the existence of positive solutions, multiple solutions, sign-changing solutions, ground states and semiclassical states, see for examples, [4,11–15,17,20,21], etc.”