Differential and Integral Equations

On the exact structure of positive solutions of an Ambrosetti-Brezis-Cerami problem and its generalization in one space variable

Shin-Hwa Wang and Tzung-Shin Yeh

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Abstract

We study the exact structure of positive solutions of an Ambrosetti-Brezis-Cerami problem and its generalization in one space variable and in the classical Laplacian case. We prove the exact multiplicity result when $\lambda $ ranges over the whole interval $\left( 0,\infty \right) $ and get more detailed results of the solution curve. The proof of our exact multiplicity result uses the modified time-map techniques which can be adapted, and the exact multiplicity result can be extended to a more general $k$-Laplacian problem with $k>1.$

Article information

Source
Differential Integral Equations Volume 17, Number 1-2 (2004), 17-44.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060470

Mathematical Reviews number (MathSciNet)
MR2035493

Zentralblatt MATH identifier
1164.34364

Subjects
Primary: 34B30: Special equations (Mathieu, Hill, Bessel, etc.)
Secondary: 34B15: Nonlinear boundary value problems 34B18: Positive solutions of nonlinear boundary value problems

Citation

Wang, Shin-Hwa; Yeh, Tzung-Shin. On the exact structure of positive solutions of an Ambrosetti-Brezis-Cerami problem and its generalization in one space variable. Differential Integral Equations 17 (2004), no. 1-2, 17--44. https://projecteuclid.org/euclid.die/1356060470.


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