## Abstract and Applied Analysis

### Multiple Solutions to Elliptic Equations on ${\mathbb{R}}^{N}$ with Combined Nonlinearities

#### Abstract

In this paper, we are concerned with the multiplicity of nontrivial radial solutions for the following elliptic equations $(\mathrm{P}{)}_{\lambda }$: $-\mathrm{\Delta }u+V(x)u=\lambda Q(x){|u|}^{q-\mathrm{2}}u+Q(x)f(u),x\in {\mathbb{R}}^{N}$; $u(x)\to \mathrm{0},$ as $|x|\to +\mathrm{\infty }$, where $\mathrm{1}, $V$, and $Q$ are radial positive functions, which can be vanishing or coercive at infinity, and $f$ is asymptotically linear at infinity.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 284953, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606723

Digital Object Identifier
doi:10.1155/2014/284953

Mathematical Reviews number (MathSciNet)
MR3232832

Zentralblatt MATH identifier
07022089

#### Citation

Yang, Miaomiao; Li, Anran. Multiple Solutions to Elliptic Equations on ${\mathbb{R}}^{N}$ with Combined Nonlinearities. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 284953, 10 pages. doi:10.1155/2014/284953. https://projecteuclid.org/euclid.aaa/1412606723

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