Positive periodic solutions for fully third-order ordinary differential equations

Periodic Solutions for Some Fully Nonlinear Fourth Order Differential Equations

In this paper we present sufficient conditions for the existence of solutions to the periodic fourth order boundary value problem u(x) = f(x, u(x), u′(x), u′′(x), u′′′(x)) u(a) = u(b), i = 0, 1, 2, 3, for x ∈ [a, b], and f : [a, b] × R4 → R a continuous function. To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations w...

Anti-periodic solutions for fully nonlinear first-order differential equations

In this paper, we study the anti-periodic boundary value problems for nonlinear first-order differential equations both in finite and in infinite dimensional spaces. Several new existence results are obtained. c © 2007 Elsevier Ltd. All rights reserved.

Existence of Three Positive Solutions for a System of Nonlinear Third-order Ordinary Differential Equations

In this work, we use the Leggett-Williams fixed point theorem, we prove the existence of at least three positive solutions of a boundary-value problem for system of third-order ordinary differential equations.

Positive periodic solutions of singular systems of first order ordinary differential equations

The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our results is based on the Krasnoselskii fixed point theorem in a cone. 2011 Elsevier Inc. All rights reserved.

Positive Periodic Solutions of Systems of Second Order Ordinary Differential Equations