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.

Nonlinear Riemann Problem for Nonlinear Elliptic Systems in Sobolev Space W_(1,p)(D)

The nonlinear Riemann problems were converted into nonlinear singular integral equ ations and the existence of the solution for the problem was proved by means of contract principle.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-SEPARATED TYPE INTEGRAL BOUNDARY CONDITIONS

In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.

On the Existence of Positive Solutions for Impulsive Neutral Differential Equations

Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.

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.

STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.

LOCAL INEQUALITIES FOR SIDON SUMS AND THEIR APPLICATIONS

The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.

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.

Existence and uniqueness results for mild solutions of random impulsive abstract neutral partial differential equation over real axis

In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle.Finally an example is given to illustrate our problem.

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.

Application and Popularization of Energy Formula

In physics, there are two main energy formulas. One is kinetic energy formula and the another is Einstein equation. But kinetic energy formula can only calculate low speed motion. Einstein equation can only calculate light speed motion. The two formulas are not unified. We hope to get a unified formula. But it didn’t work. According to the principle of Lorentz contraction, we generalize the contraction of length to the contraction of mass, and obtain a unified energy formula. This is the generalized Einstein equation and the new Einstein kinetic energy formula.

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.

On Characterization of Iterative Approximation for Asymptotically Pseudocontractive Mappings

Let C be a nonempty bounded closed convex subset of a Banach space X, and T : C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}(?)[1, ∞), limn→∞ kn = 1. Fix u ∈ C. For each n ≥ 1, xn is a unique fixed point of the contraction Sn(x) = (1 - (tn)/(Lkn))u + (tn)/(Lkn)Tnx(?)x ∈ C, where {tn}(?)[0,1). Under suitable conditions, the strong convergence of the sequence{xn}to a fixed point of T is characterized.

Existence,construction and extension of continuous solutions of an iterative equation with multiplication

The iterative equation is an equality with an unknown function and its iterates,most of which found from references are a linear combination of those iterates.In this paper,we work on an iterative equation with multiplication of iterates of the unknown function.First,we use an exponential conjugation to reduce the equation on R+to the form of the linear combination on R,but those known results on the linear combination were obtained on a compact interval or a neighborhood near a fixed point.We use the Banach contraction principle to give the existence,uniqueness and continuous dependence of continuous solutions on R+that are Lipschitzian on their ranges,and construct its continuous solutions on R_(+)sewing piece by piece.We technically extend our results on R_(+)to R_(-)and show that none of the pairs of solutions obtained on R+and R_(-)can be combined at the origin to get a continuous solution of the equation on the whole R,but can extend those given on R+to obtain continuous solutions on the whole R.

APPROXIMATE INERTIAL MANIFOLDS TO THE NAVIER-STOKES EQUATIONS

In this paper,we construct an infinite family of approximate inertial manifolds for the Navier-Stokes equations.These manifolds provide higher and higher order approximations to the attractor.Our manifolds are constructed by contraction principle and therefore can be easily approximated by simple explicit functions in real computations.

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.

HYERS-ULAM-RASSIAS STABILITY OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS

In this paper, using Banach’s contraction principle, we consider the Hyers-UlamRassias stability of nonlinear partial diferential equations. An example is given to demonstrate the applicability of our results.

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.