15-64 Vitali Vougalter, Vitaly Volpert

On the existence of stationary solutions for some systems of integro-differential equations with anomalous diffusion (128K, pdf) Jul 11, 15

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Abstract. The article is devoted to the proof of the existence of solutions of a system of integro-differential equations appearing in population dynamics in the case of anomalous diffusion when the negative Laplacian is raised to some fractional power. The argument relies on a fixed point technique. Solvability conditions for elliptic operators without Fredholm property in unbouned domains along with the Sobolev inequality for a fractional Laplace operator are being used.

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