Rocky Mountain Journal of Mathematics

A sign-changing solution for the Schrödinger-Poisson equation in $\mathbb R^3$

Claudianor O. Alves, Marco A.S. Souto, and Sérgio H.M. Soares

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Abstract

We find a sign-changing solution for a class of Schr\"odinger-Poisson systems in $\mathbb {R}^3$ as an existence result by minimization in a closed subset containing all the sign-changing solutions of the equation. The proof is based on variational methods in association with the deformation lemma and Miranda's theorem.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 1 (2017), 1-25.

Dates
First available in Project Euclid: 3 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1488531891

Digital Object Identifier
doi:10.1216/RMJ-2017-47-1-1

Mathematical Reviews number (MathSciNet)
MR3619755

Zentralblatt MATH identifier
1381.35021

Subjects
Primary: 35J15: Second-order elliptic equations 35J20: Variational methods for second-order elliptic equations 35J47: Second-order elliptic systems

Keywords
Schrödinger-Poisson systems sign-changing solutions variational methods

Citation

Alves, Claudianor O.; Souto, Marco A.S.; Soares, Sérgio H.M. A sign-changing solution for the Schrödinger-Poisson equation in $\mathbb R^3$. Rocky Mountain J. Math. 47 (2017), no. 1, 1--25. doi:10.1216/RMJ-2017-47-1-1. https://projecteuclid.org/euclid.rmjm/1488531891


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