A nonlinear boundary value problem for second order differential systems

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Boundary value problem for second-order impulsive functional differential equations

This paper discusses a kind of linear boundary value problem for a nonlinear second order impulsive functional differential equations. We establish several existence results by using the lower and upper solutions and monotone iterative techniques. An example is discussed to illustrate the efficiency of the obtained result. © 2005 Elsevier Inc. All rights reserved.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

On Boundary Value Problems for Systems of Ordinary, Nonlinear, Second Order Differential Equations^)

where x and z are vectors (not necessarily of the same dimension). 1. Below, if x, f are vectors, \x\ denotes the Euclidean length of x and x-f the scalar product of x and/. In §§1—5, there will be obtained a priori bounds for the first derivatives of w-vector functions x(t) subject to second order differential inequalities. In this direction, our results are new only for n> 1. For reference an...

Generalized quasilinearization method for a second order three point boundary-value problem with nonlinear boundary conditions

The generalized quasilinearization technique is applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of three point boundary value problem for second order differential equations with nonlinear boundary conditions. Also, we improve the convergence of the sequence of iterates by establishing a convergence of order k.