Translator Disclaimer
2002 On an open problem of Ambrosetti, Brezis and Cerami
Yuanji Cheng
Differential Integral Equations 15(9): 1025-1044 (2002).

Abstract

In this paper we study the structure of all solutions to the boundary value problem, which is the open problem D of Ambrosetti, Brezis and Cerami [1] $$ -u'' = \lambda |u|^{q-1}u+|u|^{p-1}u, \quad t\in [a, b], \ \ u(a)=u(b)=0, $$ where $0 <q <1 <p,$ $ \lambda >0 .$ We obtain a complete characterization of its solutions and the bifurcation graph. By perturbation, we show also instablity of the structure of the solutions for the above problem (see Figure 3).

Citation

Download Citation

Yuanji Cheng. "On an open problem of Ambrosetti, Brezis and Cerami." Differential Integral Equations 15 (9) 1025 - 1044, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1029.34017
MathSciNet: MR1919760

Subjects:
Primary: 34B15
Secondary: 34B18, 34C23, 35B32, 35J60, 47J10

Rights: Copyright © 2002 Khayyam Publishing, Inc.

JOURNAL ARTICLE
20 PAGES


SHARE
Vol.15 • No. 9 • 2002
Back to Top