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arXiv · 2603.06127

Asymptotically linear fractional problems with mixed boundary conditions

Giovanni Molica Bisci·Alejandro Ortega·Luca Vilasi
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Abstract

We derive the existence of solutions for an asymptotically linear equation driven by the spectral fractional Laplacian operator with mixed Dirichlet-Neumann boundary conditions. When the nonlinear term $f$ is odd and a suitable relation between the perturbation parameter, the limit of $f(\cdot,t)/t$ as $t\to 0$ and the eigenvalues occurs, we establish also a multiplicity result via the pseudo-index theory related to the genus.

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Giovanni Molica Bisci, Alejandro Ortega, Luca Vilasi. 2026-03-06. Asymptotically linear fractional problems with mixed boundary conditions. https://arxiv.org/abs/2603.06127

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