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 Â âˆ†u(x) + f(|x|, u(x), v(x)) = 0 Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â inÂ B1(0) Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â âˆ†v(x) + g(|x|, u(x), v(x)) = 0, Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â u(x) = 0, v(x) = 0 on (B1(0)). Â are studied. We use the method of moving planes and maximum principles to prove the symmetry of solutions. Â Keywords: Maximum principles; Moving plane method; Radial symmetry; Narrow region principle; nonlinear system. Â AMS 2010 : 35B06, 35B09, 35J25, 35B50.