Fully nonlinear logistic equations with sanctuary

Isabeau Birindelli; Giulio Galise; Fabiana Leoni

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arXiv · 2603.29885

Fully nonlinear logistic equations with sanctuary

Isabeau Birindelli·Giulio Galise·Fabiana Leoni

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Abstract

For the fully nonlinear stationary logistic equation ${\mathcal F}(x,D^2u)+\mu u=k(x)u^p$ with $p>1$ and $k(x)\geq 0$, in a bounded domain with Dirichlet boundary condition, we determine, in terms of $\mu$, the existence and uniqueness or the nonexistence of a positive solution. Furthermore, we study the asymptotic behavior of the solutions when $\mu$ approaches the boundary points of the existence range.

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Isabeau Birindelli, Giulio Galise, Fabiana Leoni. 2026-03-31. Fully nonlinear logistic equations with sanctuary. https://arxiv.org/abs/2603.29885

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