In this paper we study the nonlinear Schrödinger–Maxwell equations −\Delta u + V (x)u +φu = |u|^{p−1}u in R3, −\Delta φ = u^2 in R^3. 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 for 3 < p < 5, and V possibly unbounded below. Existence and nonexistence results are proved also when the nonlinearity exhibits a critical growth.
Ground state solutions for the nonlinear Schrodinger-Maxwell equations
AZZOLLINI, ANTONIO;
2008-01-01
Abstract
In this paper we study the nonlinear Schrödinger–Maxwell equations −\Delta u + V (x)u +φu = |u|^{p−1}u in R3, −\Delta φ = u^2 in R^3. 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 for 3 < p < 5, and V possibly unbounded below. Existence and nonexistence results are proved also when the nonlinearity exhibits a critical growth.File in questo prodotto:
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