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In this paper, we study the existence of solutions for integrodifferential Schrödinger equations of the formwhereis a nonlocal operator with a measurable kernel which satisfies ‘structural properties’, more general than the standard kernel of fractional Laplacian operator,  V  is a bounded potential, and the nonlinear termhas critical exponential growth with respect to the Trudinger–Moser inequality.

On nonlinear perturbations of a periodic integrodifferential equation with critical exponential growth