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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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.

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

First available in Project Euclid: 3 March 2017

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

Schrödinger-Poisson systems sign-changing solutions variational methods


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.

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