Azzollini, A. and Pomponio, A.:
A Note on the Ground State Solutions for the Nonlinear Schrödinger-Maxwell Equations
Bollettino dell'Unione Matematica Italiana Serie 9 2 (2009), fasc. n.1, p. 93-104, (English)
pdf (261 Kb), djvu (107 Kb). | MR 2493646 | Zbl 1173.35674
Sunto
In this paper we study the nonlinear Schrödinger-Maxwell equations $$\begin{cases} - \Delta u + V(x) u + \phi u= |u|^{p-1} u \quad & \text{in} \,\, \mathbb{R}^{3}, \\ - \Delta \phi = u^{2} & \text{in} \,\, \mathbb{R}^{3}.\end{cases}$$ 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.
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