Abstract
In this paper, we show the existence of nontrivial solutions for the following planar Choquard equation: where is the Riesz potential. We mainly consider the case that is 1‐periodic, has critical exponential growth at infinity and 0 lies in a gap of the spectrum of . There are few works in the literature concerned with such problem due to the compactness issue, appearance of the convolution term , and the difficulties aroused by the strongly indefinite characteristic and the critical exponential growth of . By employing an approximation scheme and some fine estimates of the mountain pass minimax levels in combination with related variational arguments, we show nontrivial solution for the above strongly indefinite problem.
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