Existence and multiplicity of nontrivial solutions for Schrödinger-Bopp-Podolsky systems with critical nonlinearity in ℝ ³

Abstract This article investigates the existence and multiplicity of nontrivial solutions for Schrödinger-Bopp-Podolsky systems with critical nonlinearity in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msup> </m:math> {{\mathbb{R}}}^{3} . Under appropriate assumptions about the potential and nonlinear terms, the existence and multiplicity of solutions are obtained by using the concentration-compactness principle and the symmetric mountain pass theorem. To some extent, we generalize the previous results.