A Note on the Ground State Solutions for the Nonlinear Schrödinger-Maxwell Equations

Azzollini, A.; Pomponio, A.

Bollettino dell'Unione Matematica Italiana, Tome 2 (2009), p. 93-104 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

In this paper we study the nonlinear Schrödinger-Maxwell equations $\begin{cases}-\Delta u+V(x)u+\phi u=|u|^{p-1}u&\text{in}\,\,\mathbb{R}^{3},\\ -\Delta\phi=u^{2}&\text{in}\,\,\mathbb{R}^{3}.\end{cases}$ If $V$ is a positive constant, we prove the existence of a ground state solution $(u,\phi)$ for $2<p<5$ . The non-constant potential case is treated for $3<p<5$ , and $V$ possibly unbounded below.

Publié le : 2009-02-01

MR 2493646 | Zbl 1173.35674

@article{BUMI_2009_9_2_1_93_0,
     author = {A. Azzollini and A. Pomponio},
     title = {A Note on the Ground State Solutions for the Nonlinear Schr\"odinger-Maxwell Equations},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {2},
     year = {2009},
     pages = {93-104},
     zbl = {1173.35674},
     mrnumber = {2493646},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2009_9_2_1_93_0}
}

Azzollini, A.; Pomponio, A. A Note on the Ground State Solutions for the Nonlinear Schrödinger-Maxwell Equations. Bollettino dell'Unione Matematica Italiana, Tome 2 (2009) pp. 93-104. http://gdmltest.u-ga.fr/item/BUMI_2009_9_2_1_93_0/

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