Positive solutions to p-Laplace reaction-diffusion systems with nonpositive right-hand side - Maciejewski, Mateusz (Topological Methods in Nonlinear Analysis, 2015)
The aim of the paper is to show the existence of positive solutions to the elliptic system of partial differential equations involving the p-Laplace operator \[ cases -Δ_p u_i(x) = f_i(u_1 (x),u_2(x),…,u_m(x)), & xΩ, 1≤ i≤ m, u_i(x)≥ 0, & xΩ, 1≤ i≤ m, u(x) = 0, & xΩ. cases \] We consider the case of nonpositive right-hand side f_i, i=1,…,m. The sufficient conditions entails spectral bounds of the matrices associated with f=(f_1,…,f_m). We employ the degree theory from CwMac for tangent perturbations of maximal monotone operators in Banach spaces.