SEMICLASSICAL STATES FOR COUPLED SCHRÖDINGER–MAXWELL EQUATIONS: CONCENTRATION AROUND A SPHERE

By D. Ruiz. 2005

143 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/08f13c2ab36455c99802ae2ad028d70e86f226e9

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Citations in the corpus

On Schrödinger-Poisson Systems (2008, methodology): “First, in Section 3, we carry out this program by reporting some recent results from [ 16 ] and [4], dealing with the existence of multiple solutions of (SP) in the autonomous case, namely when, say, V (x) ≡ K(x) ≡ 1. We shall see that for 2 0. On the other hand, for 1 16 ].”
On Concentration of Positive Bound States for the Schrödinger-Poisson Problem with Potentials (2008, background): “As in [7] it is easy to see that for all v ∈ H(1)(R(3)) the Poisson equation −∆φ = K(x)v(2) has a unique positive solution φK,v ∈ D(1,2)(R(3)) given by φK,v(x) = ∫”
The Schrödinger–Poisson equation under the effect of a nonlinear local term (2006, methodology): “In [14,24] it is proved the existence of a certain solution wλ of (24) for λ small and p < 11/7.”
On the Schrödinger–Poisson–Slater System: Behavior of Minimizers, Radial and Nonradial Cases (2009, background): “First of all, if u is a radial function, φu is also radial, and can be written as (see [13, 24]): φu(r) = 1 r ∫ +∞ 0 u(2)(s)smin{r, s} ds.”
Multiplicity and concentration of positive solutions for the fractional Schrödinger–Poisson systems with critical growth (2017, unknown): “For more results on the semiclassical states we refer the readers to [3,27,30,33,48] and the references therein.”
Multiple positive solutions for a Schr\"odinger-Poisson-Slater system (2009, background): “[13, 23] in which the case with Ω = R3 and λ→ 0+ is considered), we have introduced the parameter λ > 0 which takes a role also in a bounded domain, at least for small values of p.”