ORDERING CONTRACTION MAPPING PRINCIPLE AND APPLICATIONS

This paper establishes an ordering contraction mapping principle for increasing mapping in partial ordering metric spaces, and applies it to prove the existence and uniqueness of fixed point for some nonlinear operators controlled by a linear operator and phi-concave operator in a partial ordering Banach space. Therefore, this two results are unified.

THE EXISTENCE AND UNIQUENESS OF SOLUTION FOR A CLASS OF STOCHASTIC FUNCTIONAL EQUAFIONS ON S.P.SPACE

This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the ekistence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.

BOUNDARY VALUE PROBLEM FOR DEGENERATE AND SINGULAR p-LAPLACIAN SYSTEMS

In this article, using the contraction mapping principle and the shooting method, the authors obtain the existence and uniqueness of the local solution and the global solution to a class of quasilinear elliptic systems with p-Laplacian as its principal. They also obtain the continuous dependence of the solutions on the boundary data.

A Kind of Boundary Value Problems for Stochastic Differential Equations

In this paper we discuss stochastic differential equations with a kind of periodic boundary value conditions（in sense of mean value）. Appealing to the decomposition of equations, the existence of solutions is obtained by using the contraction mapping principle and Leray-Schauder fixed point theorem, respectively.

Asymptotic Stability of Singular Solution for Camassa-Holm Equation

The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability of the explicit singular solution of Camassa-Holm equation.

A Periodic Dividend Problem with Inconstant Barrier in Markovian Environment

Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.

The Existence of Solutions for the Problem in the Optical Lattice with Nonlocal Nonlinearity

We address the impact of nonlocality in the physical features exhibited by solitons supported by Kerr-type nonlinear media with an imprinted optical lattice. We discuss the solitons solution for a class of nonlinear SchrSdinger equations in the optical lattice with nonlocal nonlinearity. We also show via a uniform priori estimate that existence and uniqueness of the global solution for the initial problem.

EXISTENCE AND UNIQUENESS OF ALMOST PERIODIC SOLUTION TO A SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

In this paper, the existence of almost periodic solution to a second order nonlinear equation is investigated by contraction mapping principle under some conditions. It ought to be noted that using Schauder fixed point theorem to discuss such a problem will cause a failure.

ON THE PLANE STRESS BOUNDARY VALUE PROBLEM OF QUASI-STATIC LINEAR THERMOELASTICITY

he stress boundary value problem of quasi-static linear thermoelasticity is discussed. The thermoelastic systems on bounded simply-connected domain is decoupled. The decoupled temperature equation is investigated by using accurate estimation and the contractive mapping principle. Representation of solution of the field equation is obtained, and some solvability results are proved.