Electron. J. Diff. Equ., Vol. 2016 (2016), No. 223, pp. 1-14.

Existence and behavior of positive solutions to elliptic system with Hardy potential

Lei Wei, Xiyou Cheng, Zhaosheng Feng

In this article, we study a class of elliptic systems with Hardy potentials. We analyze the possible behavior of radial solutions to the system when $p,t>1$, $q,s>0$ and $\lambda,\mu>(N-2)^2/4$, and obtain the existence of positive solutions to the system with the Dirichlet boundary condition under certain conditions. When $\lambda,\mu\leq 0$, p,t>1 and q,s>0, we show that any radial positive solution is decreasing in r.

Submitted January 12, 2016. Published August 17, 2016.
Math Subject Classifications: 35B40, 35J25.
Key Words: Elliptic system; Hardy potential; existence; positive solution; blow up.

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Lei Wei
School of Mathematics and Statistics
Jiangsu Normal University
Xuzhou 221116, China
email: wlxznu@163.com
  Xiyou Cheng
School of Mathematics and Statistics
Lanzhou University
Lanzhou 730000, China
email: chengxy@lzu.edu.cn
Zhaosheng Feng
Department of Mathematics
University of Texas-Rio Grande Valley
Edinburg, TX 78539, USA
email: zhaosheng.feng@utrgv.edu

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