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September/October 2021 Schrödinger-Maxwell systems with interplay between coefficients and data
David Arcoya, Lucio Boccardo, Luigi Orsina
Adv. Differential Equations 26(9/10): 505-534 (September/October 2021).

Abstract

In this paper, we prove existence of a solution $(u,\varphi)$ in $W_0^{1,2}(\Omega) \times W_0^{1,2}(\Omega)$ for the Schrödinger-Maxwell type system $$ (*)\quad \left\{ \begin{array}{cl} -{\rm div} (M(x) \nabla u) + a(x)\,\varphi \,|u|^{r-2} u = f(x)\,, & \mbox{in $\Omega$,} \\ -{\rm div}(N(x) \nabla \varphi) = a(x) |u|^{r}\,, & \mbox{in $\Omega$,} \\ u = \varphi = 0\,, & \mbox{on $\partial\Omega$,} \end{array} \right. $$ with $M$ and $N$ bounded, uniformly elliptic matrices, $r > 1$, $a(x)$ in $L^{1}(\Omega)$ and $f$ such that $|f(x)| \leq Q\,a(x)$ for some positive constant $Q$.

Citation

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David Arcoya. Lucio Boccardo. Luigi Orsina. "Schrödinger-Maxwell systems with interplay between coefficients and data." Adv. Differential Equations 26 (9/10) 505 - 534, September/October 2021.

Information

Published: September/October 2021
First available in Project Euclid: 12 August 2021

Subjects:
Primary: 35J50, 35J67

Rights: Copyright © 2021 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.26 • No. 9/10 • September/October 2021
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