Existence of positive solutions for second order m-point boundary value problems

Abstract

Abstract. Let α, β, γ, δ ≥ 0 and := γβ + αγ + αδ > 0. Let ψ(t) = β + αt, φ(t) = γ + δ − γt, t ∈ [0, 1]. We study the existence of positive solutions for the m-point boundary value problemWe show the existence of positive solutions if f is either superlinear or sublinear by a simple application of a fixed point theorem in cones. Our result extends a result established by Erbe and Wang for two-point BVPs and a result established by the author for three-point BVPs.1. Introduction. The study of multi-point boundary value problems for linear second order ordinary differential equations was initiated by Il'in and Moiseev [6]. Motivated by [6], Gupta [4] studied certain three-point boundary value problems for nonlinear ordinary differential equations. Since then, more general nonlinear multi-point boundary value problems have been studied by several authors. We refer the reader to [4][5][6][8][9][10] for some relevant references.

On the existence of multiple solutions for a nonlocal BVP with vector-valued response

“…Tsamatos ( [8]), R. Ma ([19]) and R. Ma and N. Castaneda ( [20]). In [21] R. Ma presents the extension of Erbe's and Wang's results for twopoint BVPs and his own results for three-point BVPs. That paper is devoted to the existence of positive solutions for the m-point boundary value problem            u + h(t)f (u) = 0 for 0 < t < 1,…”

“…Then the integral condition (3) does not give, in general, the positivity of the corresponding integral operator. Our investigations are justified by the large number of papers associated with similar problems, among others, [1], [4], [5], [6], [11], [15], [16], [21], [27]. This work is motivated mainly by [17].…”

Existence and properties of solutions for boundary value problems based on the nonlinear reactor dynamics

“…The research on multipoint boundary value problems containing nonlinear ODEs has been enjoying of increasing interests for many years (see [12,28,29,31,34,35,41,42,44,49] and references therein). Many real-life problems modeled by such BVPs arise in various areas of applied mathematics: in chemical or physical phenomena, in the electrohydrodynamics and astrophysics (see, among others, [1,4,5,30]).…”

Loss of positivity in a nonlinear second order ordinary differential equations

“…We refer the reader to [3][4][5][6][7][8][9][10][11][12][13] for other recent results on nonlinear multi-point boundary value problems. This paper is mainly concerned with the existence of nonzero solutions to the generalized boundary value problem such as…”