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2004 Exactly two entire positive solutions for a class of nonhomogeneous elliptic equations
Kuan-Ju Chen
Differential Integral Equations 17(1-2): 1-16 (2004).

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.

Citation

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Kuan-Ju Chen. "Exactly two entire positive solutions for a class of nonhomogeneous elliptic equations." Differential Integral Equations 17 (1-2) 1 - 16, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1164.35302
MathSciNet: MR2035492

Subjects:
Primary: 35J60
Secondary: 35B05, 35J20

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 1-2 • 2004
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