Existence of ground state solutions for a biharmonic Choquard equation with critical exponential growth in ℝ4$$ {\mathrm{\mathbb{R}}}^4 $$

Abstract

In this paper, we study the following singularly perturbed biharmonic Choquard equation: where is a parameter, , ∗ is the convolution product in , and is a continuous real function. is the primitive function of , and has critical exponential growth in the sense of the Adams inequality. By using variational methods, we establish the existence of ground state solutions when small enough.