Existence of solutions for three-point boundary value problems for second order equations

Abstract

Abstract. Shooting methods are employed to obtain solutions of the threepoint boundary value problem for the second order equation, y = f (x, y, y ), y(x 1 ) = y 1 , y(x 3 ) − y(x 2 ) = y 2 , where f : (a, b) × R 2 → R is continuous, a < x 1 < x 2 < x 3 < b, and y 1 , y 2 ∈ R, and conditions are imposed implying that solutions of such problems are unique, when they exist.

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.…”

Existence of three solutions for multi-point boundary value problems

“…Recently, multi-point BVPs have been extensively studied by many researchers, see [5,6,7] and the references therein. In [8] (φ p (u )) + q(t) f (t, u, u ) = 0, in (0, 1),…”

Monotone and convex positive solutions for fourth-order multi-point boundary value problems

“…Owing to its importance in application, the existence of positive solutions for nonlinear second and higher order boundary value problems has been studied by many authors. We refer to recent contributions of Ma [1][2][3], He and Ge [4], Guo and Ge [5], Avery et al [6,7], Henderson [8], Eloe and Henderson [9], Yang et al [10], Webb and Infante [11,12], and Agarwal and O'Regan [13]. For survey of known results and additional references, we refer the reader to the monographs by Agarwal [14] and Agarwal et al [15].…”