Theoretical study demonstrates the existence of solutions for integro-differential equations with mixed diffusion operators, highlighting solvability criteria in unbounded domains.
The work deals with the studies of the existence of solutions of an integro-differential equation in the situation of the difference of the standard Laplacian and the bi-Laplacian in the diffusion term. The proof of the existence of solutions relies on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains.
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Vougalter et al. (2026) studied this question.
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