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In this paper, we study the following class of weighted Choquard equations align* - u = u + (_ Q (|y|) F (u (y) ) |x-y|^dy) Q (|x|) f (u) ~~in~~ ~~ and~~ u=0~~ on~~, align* where R² is a bounded domain with smooth boundary, (0, 2) and >0 is a parameter. We assume that f is a real valued continuous function satisfying critical exponential growth in the Trudinger-Moser sense, and F is the primitive of f. Let Q be a positive real valued continuous weight, which can be singular at zero. Our main goal is to prove the existence of a nontrivial solution for all parameter values except the resonant case, i. e. , when coincides with any of the eigenvalues of the operator (-, H¹₀ () ).
Kanungo et al. (Thu,) studied this question.