Positive solutions of superlinear semipositone singular Dirichlet boundary value problems

Abstract

In this paper, we study a class of superlinear semipositone singular second order Dirichlet boundary value problem. A sufficient condition for the existence of positive solution is obtained under the more simple assumptions.  2005 Elsevier Inc. All rights reserved.

Global Structure of Positive Solutions for Some Second-Order Multipoint Boundary Value Problems

“…The existence and multiplicity of nontrivial solutions for multipoint boundary value problems have been extensively considered (including positive solutions, negative solutions, or sign-changing solutions) by using the fixed point theorem with lattice, fixed point index theory, coincidence degree theory, Leray-Schauder continuation theorems, upper and lower solution method, and so on (see and references therein). On the other hand, some scholars have studied the global structure of nontrivial solutions for second-order multipoint boundary value problems (see [26][27][28][29][30][31][32] and references therein).…”

“…Motivated by [1,[26][27][28][29][30][31][32], we shall investigate the global structure of positive solutions of the boundary value problem (1). In [1], the authors only have studied the existence of positive solutions, but in this paper, we prove that the set of nontrivial positive solutions of the boundary value problem (1) possesses an unbounded connected component.…”

Existence of positive solution for a fractional order nonlinear differential system involving a changing sign perturbation

“…Generally, some perturbations and uncertainties usually exist in these real world differential models due to some uncertain physical parameters and parametrical variations in time. These perturbations and uncertainties can be introduced in the underlying mathematical model [3,5,7,9,10,15,16,18].…”

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

“…Recently, Zhang [12] considered the following singular semipositone Dirichlet boundary value problem:…”

“…Under the superlinear condition, by using the fixed point index, the authors established the existence of positive solutions for the semipositone problem (1.1). But Zhang [12] did not establish the conditions for the existence of multiple positive solutions, and also did not consider the sublinear case. This paper fills this gap in the literature, i.e, we concern with the multiple solutions of the following singular semipositone Dirichlet boundary value problem:…”