This analysis demonstrates the existence of ground state solutions in a biharmonic equation, implying critical behavior is achievable with variational methods.
This paper studies the following biharmonic Choquard equation with a local nonlinear perturbation: [Formula: see text] where [Formula: see text], [Formula: see text] is the Riesz potential and [Formula: see text] has critical exponential growth in the sense of the Adams inequality. The exponent [Formula: see text] is critical with respect to the Hardy–Littlewood–Sobolev inequality. By using variational methods, we establish the existence of a nontrivial solution or a Nehari-type ground state solution for the above equation in the doubly critical case, i.e. the appearance of both the lower critical exponent [Formula: see text] and the critical exponential growth of [Formula: see text].
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Qin et al. (2026) studied this question.
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