Positive Solutions For Boundary Value Problem Research Articles

MULTIPLE POSITIVE SOLUTIONS OF BVPS FOR SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-CARATHEODORY NONLINEARITIES

In this article, the existence of multiple positive solutions of boundary-value problems for nonlinear singular fractional order elastic beam equations is established. Here f depends on x, x′ and x″, f may be singular at t = 0 and t = 1 and f is non-Caratheodory function. The analysis relies on the well known Schauder fixed point theorem and the five functional fixed point theorems in the cones.

Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating Arguments

This paper considers fourth-order differential equations with four-point boundary conditions and deviating arguments. We establish sufficient conditions under which such boundary-value problems have positive solutions. We discuss such problems in the cases when the deviating arguments are delayed or advanced. In order to obtain the existence of at least three positive solutions, we use a fixed-point theorem due to Avery and Peterson. To the authors’ knowledge, this is a first paper where the existence of positive solutions of boundary-value problems for fourth-order differential equations with deviating arguments is discussed.

Positive solutions to a multi-point boundary value problem with delay

The paper is concerned with the existence of positive solutions for the nonlinear multi-point boundary value problems of a class of second-order delay differential equations. Our results improve some recent results obtained in [D.Q. Jiang, Multiple positive solutions for boundary value problems of second-order delay differential equations, Appl. Math. Lett. 15 (2002) 575–583; Dingyong Bai, Yuantong Xu, Existence of positive solutions for boundary-value problems of second-order delay differential equations, Appl. Math. Lett. 18 (2005) 621–630].

Existence of positive solutions for boundary-value problems of second-order delay differential equations

The paper is concerned with the existence of positive solutions for the nonlinear eigenvalue problem with singularity and the superlinear semipositone problem of second-order delay differential equations. The main results in this paper extend some of the existing literature. The proofs are based on a fixed-point theorem in cones.

Existence of positive solutions forboundary value problems of second-order functional difference equations

We prove the existence of positive solutions for boundary value problems of second-orderfunctional difference equations. The result here is the generalization of a corresponding result for ordinary difference equations.

Positive solutions of boundary-value problems for disfocal ordinary differential equations

We study the existence of positive solutions of a nonlinear eigenvalue problem for a two-point boundary-value problem for a family of second-order disfocal ordinary differential equations. We apply a cone-theoretic fixed-point theorem and obtain both sufficient conditions for the existence of positive solutions and sufficient conditions for the existence of multiple positive solutions.

Multiple positive solutions of boundary-value problems for impulsive differential equations

Multiple positive solutions of boundary-value problems for impulsive differential equations

Implementation of new iterative techniques for solutions of Thomas-Fermi and Emden-Fowler equations

Results of computational trials of recently developed iterative techniques for finding positive solutions of boundary-value problems for the Thomas-Fermi and generalized Emden-Fowler equations are presented. Proofs of convergence of iterative techniques have been established in other papers by the authors. The proofs, and therefore the iterative techniques, are based upon solutions of linear Sturm-Liouville problems related to the original nonlinear problems.

On the positive solutions of boundary-value problems for a class of nonlinear differential equations

On the positive solutions of boundary-value problems for a class of nonlinear differential equations