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.

A corrigendum was posted on August 21, 2014. It presents a proof of Lemma 2.4 with a modified assumption (F2), and without assumption (M2). This is necessary because there is no function satisying the original assumptions (M1) and (M2). See the last page of this article.

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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

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