GLOBAL EXISTENCE OF SOLUTION TO NONLINEAR INTEGRODIFFERENTIAL EQUATION IN A BANACH SPACE

Using Daher's fixed point theorem, we obtain a local existence theorem, in which the assumption is weaker than That in the Theorem 2.1 in [2]. Based on this theorem, we get a global existence theorem which is an extension of certain results for ordinary differential equations.

THE EXISTENCE OF SOLUTION TO THE FINITE ELASTODYNAMICS WITH MIXEDBOUNDARY CONDITIONS

In this paper the existence of solution to finite elastodynamics constrainted by mixed boundary conditions is derived when the hyperpotential and its gradient (for Green's strain) satisfy adequate conditions.

Existence of Solutions of a Two-Point Boundary Value Problem

A two-point boundary value problem with a non-negative parameter Q arising inthe study of surface tension induced flow of a liquid metal or semiconductor is studied. We provethat the problem has at least one solution for Q ≥ 0. This improves a recent result that theproblem has at least one solution for 0 ≤ Q ≤ 13.21.

The Global Attractor and Its Dimension Estimation of Generalized Kolmogorov-Petrovlkii-Piskunov Equation

In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.

EXISTENCE OF SOLUTIONS TO BOUNDARY VALUE PROBLEMS FOR IMPULSIVE DEFFERENTIAL EQUATIONS WITH DELAYED ARGUMENTS

In this paper,we study the existence and approximation of solution to boundary value problems for impulsive differential equations with delayed arguments.Sufficient conditions are established for the existence of a unique solution or extremal ones to the given problem.A monotone iterative technique is applied.

Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

ON TRANSMISSION PROBLEM FOR KIRCHHOFF TYPE WAVE EQUATION WITH A LOCALIZED NONLINEAR DISSIPATION IN BOUNDED DOMAIN

In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physi- cally different types of materials, one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary, while the other is a Kirchhoff type wave equation with nonlinear memory.

Global Attractors and Their Dimension Estimates for a Class of Generalized Kirchhoff Equations

In this paper, we studied the long-time properties of solutions of generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for the nonlinear source term g (u) and Kirchhoff stress term M (s) in the equation, and the existence and uniqueness of the solution are proved by using uniform prior estimates of time and Galerkin’s finite element method. Then, abounded absorption set B0k is obtained by prior estimation, and the Rellich-kondrachov’s compact embedding theorem is used to prove that the solution semigroup S (t) generated by the equation has a family of the global attractor Ak in the phase space . Finally, linearize the equation and verify that the semigroups are Frechet diifferentiable on Ek. Then, the upper boundary estimation of the Hausdorff dimension and Fractal dimension of a family of the global attractor Ak was obtained.

On a Discrete Fractional Boundary Value Problem with Nonlocal Fractional Boundary Conditions

In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem.

FRACTIONAL INTEGRAL INEQUALITIES AND THEIR APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS

In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.

ON TRANSMISSION PROBLEM FOR VISCOELASTIC WAVE EQUATION WITH A LOCALIZED A NONLINEAR DISSIPATION

In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials, one component being a Kirchhoff type wave equation with time dependent localized dissipation which is effective only on a neighborhood of certain part of boundary, while the other being a Kirchhoff type viscoelastic wave equation with nonlinear memory

On Uniform Decay for Transmission Problem of Kirchhoff Type Viscoelastic Wave Equation

In this paper we consider the large time behavior of solutions to an n-dimensional transmission problem for two Kirchhoff type viscoelastic wave equations, that is, the wave propagation over bodies consisting of two physically different types of materials. One component is a simple elastic part while the other is a viscoelastic component endowed with a long range memory. We show that the dissipation produced by the viscoelastic part is strong enough to produce exponential or polynomial decay of the solution

Existence and Uniqueness in Shapefrom Shading

For the image of a smooth surface object fully contained within the field of view and illuminated in an arbitrary direction, this paper discusses the ekistence and uniqueness of the conditions for solving a shape-from-shading problem under the conditions that the Fourier series expansion of the image intensity contains only zero and first order terms in a polar coordinate system. Three theorems are established, one for the ekistence and two for the uniqueness of z-axis symmetric shape from shading.

On the Cauchy Problem of Evolution P-Laplacian Equations with Strongly Non-linear Sources When 1

We study the solvability of the Cauchy problem （1.1）-（1.2） for the largest possible class of initial values,for which （1.1）-（1.2） has a local solution.Moreover,we also study the critical case related to the initial value u0,for 1【p【∞.

BOUNDARY VALUE PROBLEM FOR MIXED TYPE FUNCTIONAL DIFFERENTIAL SYSTEM

We use the topological method to deal with the boundary value problem (BVP) for a mixed type functional differential system with the form = A(t)x(t) + f(t, x^t), 0 ≤t≤T, where x^t(θ) = x(t + θ), -r ≤θ≤ r. Existence principle and theorem for solutions of the BVP are obtained.