On the existence of ground states of an equation of Schrödinger–Poisson–Slater type

Abstract

We study the existence of ground states of a Schrödinger-Poisson-Slater type equation with pure power nonlinearity. By carrying out the constrained minimization on a special manifold, which is a combination of the Pohozaev manifold and Nehari manifold, we obtain the existence of ground state solutions of this system.

Ground state solutions for a Schrödinger–Poisson–Slater‐type equation with critical growth

“…Clearly, , it seems difficult to verify the condition. Inspired by Lei and Lei, 16 we establish the following result:…”

“…Very recently, Lei and Lei 16 studied the following version of the Schrödinger–Poisson–Slater system where . The authors proved that if when or when , system () has a ground state solution in via the Pohozaev manifold and Nehari manifold.…”

“…Very recently, Lei and Lei 16 studied the following version of the Schrödinger-Poisson-Slater system…”

Ground State and Symmetry Breaking of Schr¨odinger-poisson-slatter Equations

“…In recent years, extensive research has been dedicated to exploring problem (1.1), see [12,15,16,18,25,26,28]. Motivated by the aforementioned outcomes, it is logical to investigate the existence problem of solutions, both radial and nonradial, for equation (1.1) under the conditions of ω = 1 and a positive λ that differentiates between size ranges, while considering a positive Riesz potential.…”

“…It is noteworthy that the results incorporate universal consequences, whereas certain results [12,16,18,25,26] can be considered as specific cases. Specifically, we point out that when the parameters ω, N, p, q, and α in our model assume particular values, our results encompass and extend the outcomes obtained by these researchers in their specific scenarios.…”