On Schrödinger-Poisson Systems

By A. Ambrosetti. 2008

275 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/44e26df24f1ea657a584bb3569d7b13a61863090

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Schrodinger-Poisson system with steep potential well (2009, result): “Some recent results in this direction was summarized in [1].”
Standing waves of nonlinear Schrödinger equations with the gauge field (2012, result): “7) can be compared to recent interesting studies (see [1,3,6,12] and references therein) on the Schrödinger–Poisson equation u − ωu − μ ( 1 |x| ∗ |u| 2 ) u + |u|q−2u = 0 in R3, (1.”
Existence and multiplicity of solutions for Schrödinger–Poisson equations with sign-changing potential (2015, background): “Ambrosetti and Ruiz [2] and Ambrosetti [3] considered problem (SP )1 with a parameter, i.”
Existence and asymptotic behavior of sign-changing solutions for the nonlinear Schrödinger–Poisson system in $${\mathbb{R}^3}$$R3 (2015, background): “We next prove that Z is closed in [0,1].”
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.”
Positive solutions for some non-autonomous Schrödinger–Poisson systems (2010, background): “1 generalizes a result proved in [1], where, under the assumptions (a1), (a2), (K) and (1.”
On ground state solutions for the Schrödinger–Poisson equations with critical growth (2014, background): “[5] A.”
The concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system (2017, unknown): “See [1,25,36,44,48] and the references therein for the existence of solutions.”
Infinitely many sign-changing solutions for the nonlinear Schrödinger–Poisson system (2014, methodology): “1, for any q ∈ [2, 6], there exists mq > 0 such that ‖u±‖q = inf w∈P∓ ‖u − w‖q ≤ mq inf w∈P∓ ‖u − w‖E = mqdist(u, P∓).”
Fractional Schrödinger–Poisson Systems with a General Subcritical or Critical Nonlinearity (2015, unknown): “See also [1] and the references therein.”