SYMMETRY OF SOLUTIONS OF SYSTEM OF NONLINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS IN BALL - Dhaigude, D.B. (Journal of Global Research in Mathematical Archives(JGRMA), 2015)
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.