Radial symmetry of positive solutions for nonlinear elliptic boundary value problems

D.B. Dhaigudea and D.P. Patilb,*

Radial symmetry of positive solutions for nonlinear elliptic boundary value problems

Authors :

D.B. Dhaigude^a and D.P. Patil^b,*

Author Address :

^aDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004 (M.S.) India.
^b Department of Mathematics, Art’s, Science and Commerce College, Saikheda-422009, Tal Niphad. Dist: Nasik (M.S.) India.

*Corresponding author.

Abstract :

The aim of this paper is to study the symmetry properties of positive solutions of nonlinear elliptic boundary value problems of type
$$Delta u+ f(|x|,u, abla u)= 0,,, ext{in},,, R^{n}.$$
egin{equation*}
u(x) ightarrow 0 ,, ext{as},,, |x| ightarrow infty
end{equation*}

We employ the moving plane method based on maximum principle on unbounded domains to obtain the result on symmetry.

Keywords :

Maximum principle; Moving plane method; Semilinear elliptic boundary value problems.

DOI :

Article Info :

Received : May 10, 2014; Accepted : October 29, 2014.