Fully nonlinear logistic equations with sanctuary

2026/03/31 by Isabeau Birindelli, Giulio Galise, Fabiana Leoni
Mathematics · #math.AP #msc:35J60 #msc:35D40 #msc:35P30

paper · pdf

19 pages

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

For the fully nonlinear stationary logistic equation \mathcal F(x,D²u)+μu=k(x)u^p with p>1 and k(x)≥ 0, in a bounded domain with Dirichlet boundary condition, we determine, in terms of μ, the existence and uniqueness or the nonexistence of a positive solution. Furthermore, we study the asymptotic behavior of the solutions when μ approaches the boundary points of the existence range.

Citations

• Boundedness of solutions of nonautonomous degenerate logistic equations
• Removable singularities for degenerate elliptic Pucci operators
• First eigenvalue and Maximum principle for fully nonlinear singular operators

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