Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 148, pp. 1-13.
Title: Existence and multiplicity of solutions for a degenerate nonlocal
elliptic differential equation
Authors: Nguyen Thanh Chung (Quang Binh University, Dong Hoi, Vietnam)
Hoang Quoc Toan (Hanoi Univ. of Science, , Vietnam)
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).
Thi is necessary because there is no function satisying the original
assumptions (M1) and (M2). See the last page of this article.