Abstract
We study existence of solutions for the singular system of Schrödinger-Maxwell equations
Here \(r > 1\), \(0< \theta < 1\), and \(f(x) \ge 0\) belongs to suitable Lebesgue spaces. We will also prove that the solution \((u,\psi )\) is a saddle point of a suitable functional.
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References
Arcoya, D., Boccardo, L., Orsina, L.: Schrödinger-Maxwell systems with interplay between coefficients and data. Adv. Differ. Equ. 26, 505–534 (2021)
Benci, V., Fortunato, D.: An eigenvalue problem for the Schrödinger-Maxwell equations. Topol. Methods Nonlinear Anal. 11, 283–293 (1998)
Boccardo, L.: The Fatou lemma approach to the existence in quasilinear elliptic equations with natural growth terms. Complex Var. Elliptic Equ. 55, 445–453 (2010)
Boccardo, L.: Elliptic systems of Schrödinger type in the spirit of Benci-Fortunato. Adv. Nonlinear Stud. 15, 321–331 (2015)
Boccardo, L., Imparato, P., Orsina, L.: Nonlinear weighted elliptic equations with Sobolev weights. Boll. Unione Mat. Ital. 15, 503–514 (2022)
Boccardo, L., Orsina, L.: Semilinear elliptic equations with singular nonlinearities. Calc. Var. Partial Differ. Equ. 37, 363–380 (2010)
Boccardo, L., Orsina, L.: A variational semilinear singular system. Nonlinear Anal. 74, 3849–3860 (2011)
Boccardo, L., Orsina, L.: Regularizing effect for a system of Schrödinger-Maxwell equations. Adv. Calc. Var. 11, 75–87 (2018)
Boccardo, L., Orsina, L.: A semilinear system of Schrödinger-Maxwell equations. Nonlinear Anal. 194, 111453, 17 (2020)
Boccardo, L., Orsina, L.: Existence results for a system of Kirchhoff-Schrödinger-Maxwell equations. Mediterr. J. Math. 17, 82 (2020)
Cirmi, G.R.: Regularity of the solutions to nonlinear elliptic equations with a lower-order term. Nonlinear Anal. 25, 569–580 (1995)
Durastanti, R.: Regularizing effect for some \(p\)-Laplacian systems. Nonlinear Anal. 188, 425–438 (2019)
Stampacchia, G.: Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus. Ann. Inst. Fourier (Grenoble) 15, 189–258 (1965)
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L.B. and L.O. wrote the main manuscript text and reviewed the manuscript.
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Boccardo, L., Orsina, L. A Singular System of Schrödinger-Maxwell Equations. Mediterr. J. Math. 21, 94 (2024). https://doi.org/10.1007/s00009-024-02632-1
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DOI: https://doi.org/10.1007/s00009-024-02632-1