Differential and Integral Equations

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

Kuan-Ju Chen

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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

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

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35J20: Variational methods for second-order elliptic equations


Chen, Kuan-Ju. Exactly two entire positive solutions for a class of nonhomogeneous elliptic equations. Differential Integral Equations 17 (2004), no. 1-2, 1--16. https://projecteuclid.org/euclid.die/1356060469

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