## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Multiple positive solutions for a nonlinear elliptic equation in weighted Sobolev space

Amira Obeid

#### Abstract

In this paper, we consider the problem (${\cal P}_{\lambda}$) in the setting of a weighted Sobolev space $W^{1, p}(\Omega, \omega)$, where $\omega$ is a weight function defined on the unbounded domain $\Omega$. The study is based on the variational methods and critical point theory. We show the existence of at least two nonnegative solutions, one with negative energy, the other one with energy which changes sign at a certain value of the positive parameter $\lambda$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 13, Number 2 (2006), 325-340.

Dates
First available in Project Euclid: 19 May 2006

https://projecteuclid.org/euclid.bbms/1148059467

Digital Object Identifier
doi:10.36045/bbms/1148059467

Mathematical Reviews number (MathSciNet)
MR2259911

Zentralblatt MATH identifier
1132.35371

Subjects
Primary: 34B15: Nonlinear boundary value problems

#### Citation

Obeid, Amira. Multiple positive solutions for a nonlinear elliptic equation in weighted Sobolev space. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 2, 325--340. doi:10.36045/bbms/1148059467. https://projecteuclid.org/euclid.bbms/1148059467