Solitary wave of ground state type for a nonlinear Klein–Gordon equation coupled with Born–Infeld theory in $\mathbb{R}^{2}$

Abstract

In this paper we prove the existence of nontrivial ground state solution for a nonlinear Klein–Gordon equation coupled with Born–Infeld theory in $\mathbb{R}^{2}$ involving unbounded or decaying radial potentials. The approach involves variational methods combined with a Trudinger–Moser type inequality and a symmetric criticality type result.

Keywords

• klein–gordon equation
• born–infeld theory
• trudinger–moser inequality
• unbounded or decaying radial potentials
• critical exponential growth
• mountain-pass theorem