Diffusive logistic equations with harvesting and heterogeneity under strong growth rate
Saeed Shabani Rokn-e-vafa, Hossein Tehrani · Advances in Nonlinear Analysis · 2017
Abstract We consider the equation - Δ u = a u - b ( x ) u 2 - c h ( x ) in Ω , u = 0 on ∂ Ω , -\Delta u=au-b(x)u^{2}-ch(x)\quad\text{in }\Omega,\qquad u=0\quad\text{on }% \partial\Omega, where Ω is a smooth bounded domain in ℝ N {\mathbb{R}^{N}} , b ( x ) {b(x)} and h ( x ) {h(x)} are nonnegative functions, and there exists Ω 0 ⊂ ⊂ Ω {\Omega_{0}\subset\subset\Omega} such that { x : b ( x ) = 0 } = Ω ¯ 0