## Differential and Integral Equations

### Exactly two entire positive solutions for a class of nonhomogeneous elliptic equations

Kuan-Ju Chen

#### Abstract

In this paper, we study the nonhomogeneous elliptic equations $-\Delta u(x)+u(x)=\lambda (f(x,u)+h(x))$ in ${\mathbb R}^{N}$, where $f(x,u)$ and $h(x)$ satisfy some assumptions. We use variational methods to obtain the existence results and give a clever argument to establish the exact number of solutions. In addition to a lack of compactness the main difficulty to overcome is the degenerated structure of the set of possible critical points.

#### Article information

Source
Differential Integral Equations Volume 17, Number 1-2 (2004), 1-16.

Dates
First available in Project Euclid: 21 December 2012