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Journal of Applied Mathematics and Computing

, Volume 38, Issue 1–2, pp 145–159 | Cite as

The existence of multiple positive solutions for a class of semipositone Dirichlet boundary value problems

  • Minling Zhong
  • Xinguang ZhangEmail author
Open Access
Article

Abstract

In this paper, we consider the existence of multiple positive solutions for the following singular semipositone Dirichlet boundary value problem:
$$\left\{\begin{array}{l}-x''(t)=p(t)f(t, x) +q(t),\quad t\in(0,1),\\[4pt]x(0) =0,\qquad x(1) = 0,\end{array}\right.$$
where p:(0,1)→[0,+∞) and f:[0,1]×[0,+∞)→[0,+∞) are continuous, q:(0,1)→(−∞,+∞) is Lebesgue integrable. Under certain local conditions and superlinear or sublinear conditions on f, by using the fixed point theorem, some sufficient conditions for the existence of multiple positive solutions are established for the case in which the nonlinearity is allowed to be sign-changing.

Keywords

Singular boundary value problem Semipositone Positive solutions Fixed point Cone 

Mathematics Subject Classification (2000)

34B15 34B25 

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.School of InformaticsGuangdong University of Foreign StudiesGuangzhouChina
  2. 2.School of Mathematical and Informational SciencesYantai UniversityYantaiChina

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