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Semiclassical ground state solutions for critical Schrödinger-Poisson systems with lower perturbations. (English) Zbl 1436.35078

The paper under review deals with the study of a class of singularly perturbed Schrödinger-Poisson systems in the three-dimensional space. The reaction is a general nonlinearity, which satisfies neither the Ambrosetti-Rabinowitz growth condition nor global monotonicity assumptions. The main result of this paper establishes the existence of a semiclassical ground state solution with exponential decay at infinity. The authors also study the asymptotic analysis of these solutions as the parameter goes to zero. The paper is well written and the reviewer believes that the techniques introduced in this paper can be applied to the qualitative and asymptotic analysis of solutions for other classes of nonlinear systems.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J10 Schrödinger operator, Schrödinger equation
35J47 Second-order elliptic systems
35Q55 NLS equations (nonlinear Schrödinger equations)
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