Electron. J. Diff. Equ., Vol. 2013 (2013), No. 148, pp. 1-13.

Existence and multiplicity of solutions for a degenerate nonlocal elliptic differential equation

Nguyen Thanh Chung, Hoang Quoc Toan

Abstract:
Using variational arguments, we study the existence and multiplicity of solutions for the degenerate nonlocal differential equation
$$\displaylines{
 - M\Big(\int_\Omega |x|^{-ap}|\nabla u|^p\,dx\Big)\operatorname{div}
 \Big(|x|^{-ap}|\nabla u|^{p-2}\nabla u\Big)
 = |x|^{-p(a+1)+c} f(x,u) \quad \hbox{in } \Omega,\cr
 u =  0 \quad \hbox{on } \partial\Omega,
 }$$
where $\Omega \subset \mathbb{R}^N$ ($N \geq 3$) and the function M may be zero at zero.

Submitted October 23, 2012. Published June 27, 2013.
Math Subject Classifications: 35J60, 35B38, 35J25.
Key Words: Degenerate nonlocal problems; existence o solutions; multiplicity; variational methods.

Show me the PDF file (267 KB), TEX file, and other files for this article.

Nguyen Thanh Chung
Dept. Science Management and International Cooperation
Quang Binh University, 312 Ly Thuong Kiet
Dong Hoi, Quang Binh, Vietnam
email: ntchung82@yahoo.com
Hoang Quoc Toan
Department of Mathematics, Hanoi University of Science
334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
email: hq_toan@yahoo.com

Return to the EJDE web page