Existence of Positive Solution to p-Laplace System
Yan Bing · Journal of Hebei North University · 2010
The existence of positive solutions to p-Laplace nonlinear elliptic system with Dirichlet boundary conditions is investigated.First,with the symmetry of the p-Laplace system and Mountain Pass Theorem,the form solution to the corresponding single equation of the original system is obtained and its positiveness is proved.The positive sup-solution to the original system is obtained.Second,the appropriate mapping is structured with the solution to decoupled system in the intervals of sub-super solutions.Finally,with the Leray-Schauder's fixed point theorem,the existence of positive solutions is obtained.