## Differential and Integral Equations

### Two positive solutions for a class of nonhomogeneous elliptic equations

Louis Jeanjean

#### Abstract

In this paper we develop an original variational approach which allows us to prove the existence of two positive solutions for a class of semilinear nonhomogeneous elliptic equations set on $\mathbb{R}^{N}$. 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 10, Number 4 (1997), 609-624.

Dates
First available in Project Euclid: 1 May 2013

https://projecteuclid.org/euclid.die/1367438634

Mathematical Reviews number (MathSciNet)
MR1741765

Zentralblatt MATH identifier
0890.35048

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J20: Variational methods for second-order elliptic equations

#### Citation

Jeanjean, Louis. Two positive solutions for a class of nonhomogeneous elliptic equations. Differential Integral Equations 10 (1997), no. 4, 609--624. https://projecteuclid.org/euclid.die/1367438634