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

Abstract

In this paper, we consider the existence of multiple positive solutions for the following singular semipositone Dirichlet boundary value problem:whereis 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.

Some Existence Results of Positive Solution to Second-Order Boundary Value Problems

“…For a small sample of such work, we refer the reader to the monographs of Agarwal [1], Agarwal et al [2], and Guo and Lakshmikantham [3], the papers of Avery et al [4] and Henderson and Thompson [5], and references therein along this line. In the literature, many attempts have been made by researchers to develop criteria which guarantee the existence and uniqueness of positive solutions to ordinary differential equations; this subject has attracted a lot of interests; see, for example, Cid et al [6], Ehme [7], Ehme and Lanz [8], Ibrahim and Momani [9], Kong [10], Ma and An [11], Zhang and Liu [12], Zhang et al [13], and Zhong and Zhang [14].…”