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

In this paper, we study the following singularly perturbed biharmonic Choquard equation: ε4Δ2u+V(x)u=εμ−41|x|μ∗F(u)f(u)inℝ4,$$ {\varepsilon}&#x0005E;4{\Delta}&#x0005E;2u&#x0002B;V(x)u&#x0003D;{\varepsilon}&#x0005E;{\mu -4}\left(\frac{1}{{\left&#x0007C;x\right&#x0007C;}&#x0005E;{\mu }}\ast F(u)\right)f(u)\kern0.30em \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}&#x0005E;4, $$ where ε>0$$ \varepsilon >0 $$ is a parameter, 0<μ<4$$ 0<\mu <4 $$, ∗ is the convolution product in ℝ4$$ {\mathrm{\mathbb{R}}}&#x0005E;4 $$, and V(x)$$ V(x) $$ is a continuous real function. F(u)$$ F(u) $$ is the primitive function of f(u)$$ f(u) $$, and f$$ f $$ has critical exponential growth in the sense of the Adams inequality. By using variational methods, we establish the existence of ground state solutions when ε>0$$ \varepsilon >0 $$ small enough. [ABSTRACT FROM AUTHOR]