Singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations

Singular Higher Order Boundary Value Problems for Ordinary Differential Equations

This paper is somewhat of an extension of the recent work done by Kunkel [6]. Kunkel looked at an extension of Rachu̇nková and Rachu̇nek’s work where they studied a second order singular boundary value problem for the discrete p-Laplacian, φp(x) = |x|x [7]. Kunkel’s results extend theirs to the second order differential case, but only for p = 2, i.e. φ2(x) = x. In this paper, we extend Kunkel’s w...

Existence of Solutions for a Class of Third Order Quasilinear Ordinary Differential Equations with Nonlinear Boundary Value Problems

In this paper, we are concerned with the third-order quasilinear ordinary differential equation (Φp(u)) = f(t, u, u′, u′′), 0 < t < 1, with the nonlinear boundary conditions u(0) = 0, g(u′(0), u′′(0)) = A, h(u′(1), u′′(1)) = B or u(0) = C, L(u′(0), u′(1)) = 0, R(u′(0), u′(1), u′′(0), u′′(1)) = 0, where A,B, C ∈ R,Φp(u) = |u|p−2u(p > 1), f : [0, 1]× R → R is continuous, g, h, L : R → R, R : R → ...

INVESTIGATION OF BOUNDARY LAYERS IN A SINGULAR PERTURBATION PROBLEM INCLUDING A 4TH ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we investigate a singular perturbation problem including a fourth order O.D.E. with general linear boundary conditions. Firstly, we obtain the necessary conditions of solution of O.D.E. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

The variational iteration method for a class of tenth-order boundary value differential equations

Multiplicity in Nonlinear Boundary Value Problems for Ordinary Differential Equations

We provide conditions for the existence of multiple solutions of two-point boundary value problems for a system of two nonlinear second-order ordinary differential equations. AMS Subject Classifications: 34B15.