Positive solutions for three-point boundary value problems with a non-well-ordered upper and lower solution condition

In this work, by using the fixed point index method, some existence results for positive solutions of certain three-point boundary value problems are obtained under a non-well-ordered upper and lower solution condition.     

具超前变元的二阶微分方程三点边值问题的正解

§ 1　 IntroductionRecently,certain three-point boundary value problems for nonlinear ordinarydifferential equations have been studied by many authors[1— 6] .However,few papers havebeen published on the same problems for nonlinear functional differential equations.In thispaper,we are concerned with the following second order differential equation with anadvanced argumentu″(t) +λa(t) f(u(h(t) ) ) =0 ,t∈ (0 ,1 ) (1 .1 )with the three-point boundary conditionsu(0 ) =0 ,αu(η) =u(1 ) ,(1 .2 )…     

Multiple solutions to a three-point boundary value problem for higher-order ordinary differential equations

In this paper, we provide sufficient conditions for the existence of at least three solutions to a three-point boundary value problem for higher-order ordinary differential equations. The nonlinear term f in the differential equation under consideration may depend on higher-order derivatives of arbitrary order and this is where the main novelty of this work lies. By applying the two pairs of upper and lower solutions method of Henderson and Thompson, as well as degree theory, the existence of at least three solutions of the problem is given.     

Existence and convergence of solutions of singular boundary value problems for second order ordinary differential equations and applications

In this paper,we consider the singular boundary value problems for second order quasilinear ordinary differential equations and prove existence and convergence on second order perturbation terms.The result is applied to solve the Riemann problem for 2×2 hyperbolic conservation laws,which is a partial differential equation arising in applied mathematical area.     

Two-point and three-point boundary value problems for n th-order nonlinear differential equations

In this article, we are concerned with existence and uniqueness of solutions of four kinds of two-point boundary value problems for nth-order nonlinear differential equations by “Shooting” method, and studied existence and uniqueness of solutions of a kind of three-point boundary value problems for nth-order nonlinear differential equations by “Matching” method.     

Positive solutions for systems of nonlinear discrete boundary value problems

Existence of eigenvalues yielding positive solutions for systems of second order discrete boundary value problems (two-point, three-point and generalized three-point) are established. The results are obtained by the use of a Guo–Krasnoselskii fixed point theorem in cones.     

Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations

This paper is devoted to study the existence of multiple positive solutions for the second order Dirichlet boundary value problem with impulse effects. The main results here is the generalization of Liu and Li [L. Liu, F.Y. Li, Multiple positive solution of nonlinear two-point boundary value problems, J. Math. Anal. Appl. 203 (1996) 610-625] for ordinary differential equations. Existence is established via the theory of fixed point index in cones.     

Positive solutions for a three-point boundary value problem at resonance

This paper deals with the second order three-point boundary value problem

     

Coexistence of positive solutions of nonlinear three-point boundary value and its conjugate problem

In this paper, the three-point boundary value problem

     

Multiple positive solutions of periodic boundary value problems for second order impulsive differential equations

This paper is devoted to study the existence of multiple positive solutions for the second order periodic boundary value problem with impulse effects. The main results here are the generalization of Jiang [Daqing Jiang, On the existence of positive solutions to second order periodic BVPs, Acta Math. Sci. 18 (1998) 31–35] for ordinary differential equations. Existence is established via the theory of fixed point index in cones.     

EXISTENCE OF SOLUTIONS OF STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS FOR NONLINEAR SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS IN BANACH SPACES

In this paper, the fixed point theorem is applied to investigate the existence of solutions of Sturm-Liouville boundary value problems for nonlinear second order impulsive differential equations in Banaeh spaces.     

A three-point Taylor algorithm for three-point boundary value problems

We consider second-order linear differential equations φ(x)y^″+f(x)y^′+g(x)y=h(x) in the interval (−1,1) with Dirichlet, Neumann or mixed Dirichlet-Neumann boundary conditions given at three points of the interval: the two extreme points x=±1 and an interior point x=s∈(−1,1). We consider φ(x), f(x), g(x) and h(x) analytic in a Cassini disk with foci at x=±1 and x=s containing the interval [−1,1]. The three-point Taylor expansion of the solution y(x) at the extreme points ±1 and at x=s is used to give a criterion for the existence and uniqueness of the solution of the boundary value problem. This method is constructive and provides the three-point Taylor approximation of the solution when it exists. We give several examples to illustrate the application of this technique.     

Positive solutions for boundary value problems of nonlinear fractional differential equation

In this paper, we deal with the following nonlinear fractional boundary value problem

where is the standard Riemann–Liouville fractional derivative. By means of lower and upper solution method and fixed-point theorems, some results on the existence of positive solutions are obtained for the above fractional boundary value problems.     

Smoothness of generalized solutions of boundary value problems for certain degenerate nonlinear ordinary differential equations

The variational method is applied to the study of a boundary value problem of the first kind for a class of nonlinear ordinary differential equations of order 2r with strong degeneracy at the endpoints of the interval (a, b). An inequality is obtained in which the norm of the solutionU of the problem under study in the sense ofW _p, ^r (a, b) is estimated from above by the norms of the given functions (x) andF(x).Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 882–890, June, 1998.