Existence-uniqueness theorems for three-point boundary value problems for nth-order nonlinear differential equations

Existence and uniqueness of solutions of multipoint boundary value problems for ordinary differential equations

“…Their theorems only concern the situation when (0.1) is linear and (s, m, r, p) = (1, 1, n, n). Results in the same spirit, with an nth-order (n ≥ 3) differential equation in place of (0.1), have been obtained in [4] for linear cases and in [1,2,9] for nonlinear cases. The principal result of the present paper is Theorem 3.1, which generalizes the theorems in [5][6][7].…”

“…The principal result of the present paper is Theorem 3.1, which generalizes the theorems in [5][6][7]. One can also derive as applications of this theorem various results which, in some cases, improve the theorems in [1,2,4,9]. These applications are presented in the last section.…”

“…, n}. Assume that conditions (C R e m a r k. In the special case of two-point boundary value problems of the form (0.1), (3.12) and (0.1), (3.13), Corollary 3.2 is a refinement of Theorem 4.1 in [9].…”

Theory of Differential Inequalities for Two-Point Boundary Value Problems and their Applications to Three-Point B.V.Ps Associated with n th Order Non-Linear System of Differential Equations

“…Moorty and Garner [4] extended this idea to a large class of problems. Utilising solution matching technique, Rao et al [6] modified the monotonicity condition on f of Barr and Sherman [2].…”

Five-point boundary value problems forn-th order differential equations by solution matching

“…Since then, there have been numerous papers in which solutions of twopoint boundary value problems on [a, b] were matched with solutions of two-point boundary value problems on [b, c] to obtain solutions of three-point boundary value problems on [a, c]. See, for example [Barr and Miletta 1974;Das and Lalli 1981;Henderson 1983;Moorti and Garner 1978;Rao et al 1981]. In 1973, Barr and Sherman [1973] used solution matching techniques to obtain solutions of threepoint boundary value problems for third order differential equations from solutions of two-point problems.…”