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arXiv · 2410.11615

On the solvability of parameter-dependent elliptic functional BVPs on annular-like domains

Alessandro Calamai·Gennaro Infante
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Abstract

We investigate the existence of nontrivial solutions of parameter-dependent elliptic equations with deviated argument in annular-like domains in $\mathbb{R}^{n}$, with $n\geq 2$, subject to functional boundary conditions. In particular we consider a boundary value problem that may be used to model heat-flow problems. We obtain an existence result by means of topological methods; in particular, we make use of a recent variant in affine cones of the celebrated Birkhoff--Kellogg theorem. Using an ODE argument, we illustrate in an example the applicability of our theoretical result.

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Alessandro Calamai, Gennaro Infante. 2024-10-15. On the solvability of parameter-dependent elliptic functional BVPs on annular-like domains. https://doi.org/10.3934/dcdsb.2024193

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