Positive solutions to a generalized second order three-point boundary value problem

A note on the existence of positive solutions of one-dimensional p-Laplacian boundary value problems

“…It is easy to find that (9) and (10) cannot be solved by the theorems in [8], [11], [23], [24], since Corresponding to the BVP (7), we find that ϕ(x) = x, n = 2 and f (t, x, y) = b(t)|sin y| + c(t)x + r(t), ξ 1 = R e m a r k 2. The BVP (11) cannot be covered by the results obtained in [14], [15] since f depends on x ′ . It is easy to find that (11) cannot be solved by the theorems in [11], [15], [23], [24], since…”

“…Then by an application of Theorem L1, (10) has at least one positive solution if R e m a r k 1. The BVP (9) and the BVP (10) cannot be solved by the results obtained in [14], since f depends on x ′ . It is easy to find that (9) and (10) cannot be solved by the theorems in [8], [11], [23], [24], since Corresponding to the BVP (7), we find that ϕ(x) = x, n = 2 and f (t, x, y) = b(t)|sin y| + c(t)x + r(t), ξ 1 = R e m a r k 2.…”

“…Recently, there have been many papers concerning the existence of positive solutions of BVPs for differential equations with or without p-Laplacian; we refer the readers to [1]- [3], [6]- [7], [9]- [10], [12]- [14], [16]- [19], [21]- [22], and [25].…”

Multiple Positive Solutions for a Nonlinear Three-Point Integral Boundary-Value Problem

“…Since then, nonlinear second-order three-point boundary value problems have also been studied by several authors. We refer the reader to [5,7,8,9,10,11,12,13,19,20,21,22,23,24,26,27,28,29,31,32,33,34,35,36,37,38,40,41,42] and the references therein.…”

Positive Solutions for Systems of M‐point Nonlinear Boundary Value Problems

“…In addition, we put the following assumptions on the functions f and g: The importance of positive solutions for boundary value problems, both theoretically as well as from the perspective of their applications in physical and engineering sciences, has been well documented in the literature; see, for example, [1,5,6,7,9,12,13,14,16,20,27]. While many of these referenced papers have been devoted to scalar problems, there is much emerging interest in boundary value problems for systems of differential equations [10,11,18,22,26,28], and a good deal of research has also involved positive solutions for multipoint nonlinear eigenvalue problems in both scalar and systems contexts [2,8,18,23].…”