Existence of least energy nodal solution for a Schrödinger–Poisson system in bounded domains

By Claudianor Oliveira Alves, M. Souto. 2013

152 citations recorded by the source corpus.

We prove the existence of least energy nodal solution for a class of Schrödinger–Poisson system in a bounded domain $${\Omega \subset {\mathbb{R}}^3}$$Ω⊂R3 with nonlinearity having a subcritical growth.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/e4ef0868fea7302a1be6f27a8676d341fab3a0d8

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In Applied Mathematics

1. Zhi-Qiang Wang
2. Zhaoli Liu
3. Jianjun Zhang
4. Wei Shuai
5. Qingfang Wang
6. Xianhua Tang
7. Nikolaos S. Papageorgiou
8. Thomas Bartsch

In Control and Systems Engineering

1. Zhaoli Liu
2. Zhi-Qiang Wang
3. Wei Shuai
4. Jianjun Zhang
5. Qingfang Wang

Citations in the corpus

• Infinitely many sign-changing solutions for the nonlinear Schrödinger–Poisson system (2014, methodology): “Since the approaches in [1,16,20,30], when applied to the monomial nonlinearity f (u) = |u|p−2u, are only valid for p ≥ 4, we want to provide an argument which covers the case p ∈ (3, 4) and this is the second purpose of the present paper.”
• Existence and asymptotic behavior of sign-changing solutions for the nonlinear Schrödinger–Poisson system in $${\mathbb{R}^3}$$R3 (2015, methodology): “Note that Wang and Zhou in [22] proved Mλ = ∅ by Brouwer degree, while Alves and Souto in [3] used Miranda’s theorem to prove Mλ = ∅.”