Exact multiplicity and stability of solutions of second-order Neumann boundary value problem

Hui Xing, Hongbin Chen and Xibing He

Applied Mathematics and Computation, 2014, vol. 232, issue C, 1104-1111

Abstract: The purpose of this paper is to establish the exact multiplicity and stability of solutions of the equation u″+g(x,u)=f(x) with the Neumann boundary value conditions u′(0)=u′(1)=0. Exactly three ordered solutions are obtained by taking advantage of the anti-maximum principle combined with the methods of upper and lower solutions. Moreover, we obtain that one of three solutions is negative, while the other two are positive, the middle solution is unstable, and the remaining two are stable.

Keywords: Neumann boundary value conditions; The method of lower and upper solutions; Exact multiplicity; Stability (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:1104-1111

DOI: 10.1016/j.amc.2014.01.119

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