Radial symmetry of positive solutions for nonlinear elliptic boundary value problems-Reference-Cited by-同舟云学术

Radial symmetry of positive solutions for nonlinear elliptic boundary value problems

Published:2015-01-01 Issue:01 Volume:3 Page:23-29
ISSN:2321-5666
Container-title:Malaya Journal of Matematik
language:
Short-container-title:Malaya J. Mat.

Author:

D.B. Dhaigude ,D.P. Patil

Abstract

The aim of this paper is to study the symmetry properties of positive solutions of nonlinear elliptic boundary value problems of type$$\begin{gathered}\Delta u+f(|x|, u, \nabla u)=0 \text { in } R^n . \\u(x) \rightarrow 0 \text { as }|x| \rightarrow \infty\end{gathered}$$We employ the moving plane method based on maximum principle on unbounded domains to obtain the result on symmetry.

Publisher

MKD Publishing House

Subject

Geology,Ocean Engineering,Water Science and Technology

Reference13 articles.

1. D,B. Dhaigude, D.P. Patil, Symmetry properties of solutions of nonlinear elliptic equations, Internatioumal Journil of Advences in Management, Tedinalogy and Engineering Sciences, Vol.11, 10(11), July 2013, 24 - 28.

2. A. Farina, L. Montoro and B. Sciunzi, Monotonicity and one dimensional symmetry for solutions of $-Delta_p u=f(u)$ in half space, Calculas of Variation, 43(2012), 123-145.

3. B. Gidas, W.M.Ni and L. Nirenberg. Symmetry and related properties via the maximum principle, Camm. Math. Phts., 681979), $200-243$.

4. B. Gidas, W.M.Ni and L. Nirenberg, Symmetry of Positiec Solutions of Non-linem Elliptic Equations in Rv, Mathematical Analysis and Applications Part A, ed. by L. Nachbin, adv. Math. Suppl. Stud. 7 , Academic Press, New York, 1981,369-402.

5. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Orier, Springer-Verlag, Berlin, 2001