Electron. J. Differential Equations, Vol. 2026 (2026), No. 22, pp. 1-12.

Continuous dependence for systems governed by fractional Laplacian on data and parameters

Dorota Bors

Abstract:
We study a boundary value problem governed by nonlinear equations involving the fractional Laplacian with exterior Dirichlet conditions. We establish sufficient conditions for the existence of solutions as well as their continuous dependence on the data and parameters. The proof of the main result relies on the variational formulation of the problem and exploits a saddle point structure imposed by the assumptions, in the spirit of the Ky Fan theorem.

Submitted October 4, 2025. Published March 18, 2026.
Math Subject Classifications: 35A15, 35B30, 35R11, 49J20, 93D05.
Key Words: Fractional Laplacian; minimax approach; Ky Fan theorem, continuous dependence.
DOI: 10.58997/ejde.2026.22

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Dorota Bors
Faculty of Mathematics and Computer Science
University of Lodz
S. Banacha 22, 90-238 Lodz, Poland
email: dorota.bors@wmii.uni.lodz.pl

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