Ground state solutions for the nonlinear Schrödinger-Maxwell equations
نویسندگان
چکیده
In this paper we study the nonlinear Schrödinger-Maxwell equations { −∆u+ V (x)u+ φu = |u|p−1u in R3, −∆φ = u2 in R3. If V is a positive constant, we prove the existence of a ground state solution (u, φ) for 2 < p < 5. The non-constant potential case is treated under suitable geometrical assumptions on V , for 3 < p < 5. Existence and non-existence results are proved also when the nonlinearity exhibits a critical growth.
منابع مشابه
Schrödinger-Maxwell equations with a singular potential
In this paper we find a ground state solution for the nonlinear Schrödinger-Maxwell equations { −∆u+ V (x)u+ φu = |u|p−1u in R3, −∆φ = u2 in R3. where V is a possibly singular potential and 3 < p < 5.
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