SYMMETRY OF SOLUTIONS OF SYSTEM OF NONLINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS IN BALL

Abstract

Abstract:

Symmetry results for the solution of system of nonlinear elliptic boundary value problem

 

∆u(x) + f(|x|, u(x), v(x)) = 0

                                                                  in  B1(0)

                                          ∆v(x) + g(|x|, u(x), v(x)) = 0,

 

                                 u(x) = 0, v(x) = 0 on (B1(0)).

 

are studied. We use the method of moving planes and maximum principles to prove the symmetry of solutions.

 

Keywords: Maximum principles; Moving plane method; Radial symmetry; Narrow region principle; nonlinear system.

 

AMS 2010 : 35B06, 35B09, 35J25, 35B50.