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The work deals with the existence of solutions of an integro-differential equation arising in population dynamics in the case of anomalous diffusion. The proof of existence of solutions relies on a fixed point technique. Solvability conditions for non-Fredholm elliptic operators in unbounded domains are being used.
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Vitali Vougalter, Vitaly Volpert, Existence of stationary solutions for some integro-differential equations with superdiffusion. Rend. Sem. Mat. Univ. Padova 137 (2017), pp. 185–201