Positive ground state solutions for the critical Klein–Gordon–Maxwell system with potentials

Abstract

This paper deals with the Klein-Gordon-Maxwell system when the nonlinearity exhibits critical growth. We prove the existence of positive ground state solutions for this system when a periodic potential V is introduced. The method combines the minimization of the corresponding Euler-Lagrange functional on the Nehari manifold with the Brézis and Nirenberg technique.

Infinitely many solutions for nonlinear Klein–Gordon–Maxwell system with general nonlinearity

“…For the critical growth case, that is, f (z) = μ|z| p-2 z + |z| 4 z, Cassani [6] showed that the above system has at least a radially symmetric solution when 4 < p < 6 or p = 4 provided that μ > 0 is sufficiently large. Soon after that, Carrião et al [5] also studied the existence of a radially symmetric solution for 2 < p < 6, which extended and generalized the results in [1] and [6], respectively. Recently, He [12] considered the following nonlinear Klein-Gordon-Maxwell system with non-constant external potential:…”

Multiple solutions for superlinear Klein–Gordon–Maxwell equations†

“…This type of equation has very interesting physical background which is a model to describe the nonlinear Klein–Gordon field interacting with the electromagnetic field. Along with the development of variational methods, many mathematicians used these methods to investigate the existence and multiplicity of solutions for differential equations equations(see [1, 2, 5–24, 26, 28]). In 2001, V. Benci and D. Fortunato [5] considered the following systems By using the variational methods, they obtained infinitely many solitary wave solutions when and .…”

Existence and multiplicity of solutions for Klein–Gordon–Maxwell systems with sign-changing potentials

“…Ground state solutions, semiclassical state solutions, nonradial solutions have been studied in [7][8][9][10]. The critical exponent case have also been considered in [11][12][13][14]. In [15], via the Ekeland variational principle and the mountain pass theorem, two nontrivial solutions for a nonhomogeneous Klein-Gordon-Maxwell system were got by Chen and Tang.…”