The Shooting Method and Nonhomogeneous Multipoint BVPs of Second-Order ODE

Abstract

Recommended by Kanishka PereraIn a recent paper, Sun et al. (2007) studied the existence of positive solutions of nonhomogeneous multipoint boundary value problems for a second-order differential equation. It is the purpose of this paper to show that the shooting method approach proposed in the recent paper by the first author can be extended to treat this more general problem.

Nodal Solutions of Nonlocal Boundary Value Problems

“…The existence of positive solutions of BVPs with nonlocal BCs, including three-point, multi-point, and integral BCs, have been studied extensively, see, for example, [1,4,5,6,7,8,9,15,16,24,26,28,29,31] and the references therein. In recent years, progress has also been made to the study of nodal solutions, i.e., solutions with a specific zero-counting property in (a, b), for nonlinear BVPs consisting of Eq.…”

Positive Solutions for Third Order Boundary Value Problems with p-Laplacian

“…(1.4) Under some assumptions, it was shown that there exists λ * > 0 such that BVP (1.3), (1.4) has at least one positive solution for 0 < λ < λ * and has no positive solution for λ > λ * . Later on, in [6,10,11,[13][14][15][16], this result was generalized to other problems with a parameter λ in the BCs. Here, we mention that, in all of the above work, neither the uniqueness of solutions nor the dependence of solutions on the parameter λ is studied, and only papers [10,11,16] studied the multiplicity of solutions.…”

The shooting method and positive solutions of fourth-order impulsive differential equations with multi-strip integral boundary conditions

“…To some extent, this approach has an advantage over the traditional methods. Readers can see [11][12][13][14][15][16] and the references therein for details.…”