Giulio Galise “Fully nonlinear logistic equations with sanctuary”

This talk concerns fully nonlinear stationary logistic-type equations of the form

F(x,D^2u) + μu = k(x)u^p,

with p > 1 and k(x) ≥ 0, in a bounded domain with Dirichlet boundary condition. We study the existence, uniqueness, and nonexistence of positive solutions depending on μ, and we analyze the asymptotic behavior of solutions as μ approaches the boundary points of the existence range.

This is joint work with I. Birindelli and F. Leoni.