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

By D. Ruiz. 2006

882 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/fff45fad3252228880039e7e76debbf8d4606e99

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Standing waves of nonlinear Schrödinger equations with the gauge field (2012, methodology): “In [12], Ruiz used a similar argument to obtain a solution for three dimensional nonlinear Schrödinger–Poisson equations ⎧⎨ ⎩ v − v − λφ(x)v + vp−1 = 0 in R3, φ + v2 = 0, lim |x|→∞ = 0 in R 3”
Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in $R^3$ (2013, methodology): “In [30], Ruiz proved that when 1 < p ≤ 2, (1.”
Ground state solutions for the nonlinear Schrödinger–Maxwell equations (2007, neutral): “On the other hand, nonexistence results for (SM) can be found in [14, 20].”
Existence of positive solutions to Schrödinger–Poisson type systems with critical exponent (2014, background): “3) were also possible for the case of q > 0 and f(t) = |t|s−1t (see [3, 23]).”
On ground state solutions for the Schrödinger–Poisson equations with critical growth (2014, background): “[19]).”
On the Schrödinger-Maxwell equations under the effect of a general nonlinear term (2009, background): “2]; • the fact that the result is obtained for small q is not surprising for at least two reasons: first, because small q makes, in some sense, less strong the influence of the term φu, which constitutes, in the first equation, a perturbation with respect to the classical nonlinear Schrödinger equat”
Existence and multiplicity of solutions for Schrödinger–Poisson equations with sign-changing potential (2015, background): “There has been a vast literature on the study of existence and multiplicity of solutions of system (SP )λ under various hypotheses on the potential V (x) and the nonlinearity f(x, u), see [1-3, 5, 9-14, 18, 19, 21, 22, 24-28, 31, 34, 35-37] and the references therein.”
Sign-changing radial solutions for the Schr\"odinger-Poisson-Slater problem (2011, background): “For q ≤ 2 and q ≥ 5 system (1) doesn’t admit any nontrivial solution (see [13, 20, 24]), while when q ∈ (2, 5) existence and multiplicity results have been proved using variational techniques.”
Ground State Solutions for the Nonlinear Schrödinger–Bopp–Podolsky System with Critical Sobolev Exponent (2020, neutral): “Then we look for a minimizer of the reduced functional restricted to a suitable manifold M∞μ , which was introduced by Ruiz in [24] when a = 0.”
On ground state solutions for some non-autonomous Schrödinger–Poisson systems☆ (2012, methodology): “In recent years, system (SP) has been studied widely via modern variational methods under the various hypotheses, see [1,3,5,6,19,26] and the references therein.”