## International Journal of Differential Equations

### Multiple Solutions of Quasilinear Elliptic Equations in ${\mathbb{\Bbb R}}^{N}$

Huei-li Lin

#### Abstract

Assume that $Q$ is a positive continuous function in ${\mathbb{\Bbb R}}^{N}$ and satisfies some suitable conditions. We prove that the quasilinear elliptic equation $-{\Delta }_{p}u+|u{|}^{p-2}u=Q(z)|u{|}^{q-2}u$ in ${\mathbb{\Bbb R}}^{N}$ admits at least two solutions in ${\mathbb{\Bbb R}}^{N}$ (one is a positive ground-state solution and the other is a sign-changing solution).

#### Article information

Source
Int. J. Differ. Equ., Volume 2010, Special Issue (2010), Article ID 673526, 12 pages.

Dates
Revised: 15 January 2010
Accepted: 1 March 2010
First available in Project Euclid: 26 January 2017

https://projecteuclid.org/euclid.ijde/1485399893

Digital Object Identifier
doi:10.1155/2010/673526

Mathematical Reviews number (MathSciNet)
MR2607723

#### Citation

Lin, Huei-li. Multiple Solutions of Quasilinear Elliptic Equations in ${\mathbb{\Bbb R}}^{N}$. Int. J. Differ. Equ. 2010, Special Issue (2010), Article ID 673526, 12 pages. doi:10.1155/2010/673526. https://projecteuclid.org/euclid.ijde/1485399893

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