Existence Of Radially Increasing Solutions For P-Laplace Systems With Neumann Boundary Conditions

We study the following system:where B is the unit ball in RN,N>2,v is the outer normal vector of the boundary(?)B,?1,?2>0,The p-Laplace operator defined as ?pu =div(|?u|p-2?u),p>1.In Chapter 2,we study the existence of radially increasing solution of p-Laplace sys-tems(*)with Neumann boundary condition when ?1 and ?2 are unknown.We use the variational method to prove the existence of the solution.and to determine the value of?1,?2.In Chapter 3 of this thesis,it is proved that when ?1 =?2 =1,there is at least one positive radially increasing solution for a linear elliptic system(*).In contrast with existence results for quasi-linear systems with Dirichlet boundary con-ditions,we note that when dealing with Neumann boundary conditions,there is no need at all to make growth assumptions to ensure the existence of radial positive solutions.In this thesis,we extend the problem of elliptic equations involving p-Laplace operator to quasi-linear elliptic systems,and obtain two corollaries about the existence of solutions for Henon equations.