TRICOMI PROBLEM FOR A MIXED EQUATION OF SECOND ORDER WITH DISCONTINUOUS COEFFICIENTS

This paper is devoted to the Tricomi problem for a mixed type equation of second order. The coeffcients are assumed to be discontinuous on the line where the type is changed. The unique existence of the solution to the problem is proved if the domain is small enough. Correspondingly, some estimates on the solution is also established.     

POSITIVE SOLUTION TO A CLASS OF SINGULAR FRACTIONAL BOUNDARY VALUE PROBLEMS

In this paper,we investigate the existence and uniqueness of positive solutions to a class of singular fractional boundary value problem.The existence of positive solutions to the problem is based on a fixed point theorem in partially ordered sets.     

一类非散度型非线性退化抛物方程解的存在性(英文)

In this paper, we discuss the existence of weak solutions to the initial and boundary value problem of a class of nonlinear degenerate parabolic equations in non-divergence form. Applying the method of parabolic regularization, we prove the existence of weak solutions to the problem. By carefully analyzing the approximate solutions to the problem, we make a series of estimates to the solutions and prove the weak convergence of the approximation solution sequence. Finally we testify the existence of weak solutions to the problem.     

POSITIVE SOLUTIONS TO FOURTH ORDER MULTI-POINT BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN OPERATOR

In this paper, we consider the existence of positive solutions to a singular fourth order p-Laplacian equation. By the upper and lower solution method and fixed point theorems, the existence of positive solutions to the boundary value problem is obtained under the assumption that the nonlinear term is decreasing.     

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NONLINEAR THIRD-ORDER ROBIN BOUNDARY VALUE PROBLEM WITH A TURNING POINT

The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above.     

POSITIVE SOLUTION TO SECOND-ORDER FOUR-POINT BOUNDARY VALUE PROBLEM WITH SIGN CHANGING NONLINEARITY

This paper considers the positive solution to a class of second-order four-point boundary value problem, in which the first order derivative is involved in the nonlinear term explicitly. By the fixed point theorem in cone, sufficient conditions ensuring the existence of positive solution to the problem are obtained. An example is given to illustrate the feasibility of the main results.     

ANALYSIS OF TWO-DIMENSIONAL ELECTROMAGNETIC SCATTERING BY A PERFECTLY CONDUCTING OBSTACLE IN A HOMOGENEOUS CHIRAL ENVIRONMENT

The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered.A two-dimensional direct scat- tering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach.The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated.Result on the uniqueness of the inverse problem is proved.     

一类二阶m点边值问题的正解

Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given.     

关于一个奇异Dirichlet问题的注记

The Dirichlet problem to a second order differential equation with some singularities is studied. Some existence results are established to the problem which generalize some results recently obtained by D. O‘Regan by eliminating some superfluous constrains to the problem. Also, some new results have been proven which may provide more useful information for the study of the problem.     

一类具$p$-Laplace非线性三点边值问题三个正解的存在性

This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established     

Existence of periodic and subharmonic solutions for second order functional difference equations

In this paper, by using the critical point theory, the existence of periodic and subharmonic solutions to a class of second order functional difference equations is obtained. The main approach used in our paper is variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic and subharmonic solutions of second order forward and backward difference equations.     

GLOBAL C1,2-SOLUTION TO FUNCTIONAL REACTION-DIFFUSION PROBLEM

This paper is concerned with the existence, uniqueness, comparison and dynamics problem of a functional reaction-diffusion problem. The existence and uniqueness of the global C1,2 strong solution to the problem is derived using Schauder fixed point theorem in Banach space instead of the Ascoli-Arzela theorem in the unbounded region, meanwhile, the maximal and minimal solutions are also presented by the monotone iteration method with a pair of supper and lower solutions as the initial iteration.     

具p-Laplacian二阶共振多点边值问题解的存在性(英文)

By using Mawhin＇s continuation theorem, the existence of a solution for a class of m-point boundary value problem at resonance with one-dimensional p-Laplacian is obtained. An example is given to demonstrate the main result of this paper.     

On Singular Sets of Local Solutions to p-Laplace Equations

The author proves that the right-hand term of a p-Laplace equation is zero on the singular set of a local solution to the equation. Such a result is used to study the existence of an optimal control problem.     

POSITIVE SOLUTIONS TO(k,n-k) NONHOMOGENEOUS BOUNDARYVALUE PROBLEM

By the Schauder fixed point theory,this paper establishes the existence of positive solutions to a(k,n k) m-point boundary value problem.We show that there exists a positive constant b such that the problem has at least one positive solution when the homogeneous boundary parameter is smaller than b,and no positive solution when this parameter is greater than b.     

On Singular Sets of Local Solutions to p-Laplace Equations

The author proves that the on the singular set of a local solution to existence of an optimal control problem. right-hand term of a p-Laplace equation is zero the equation. Such a result is used to study the     

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T) is assumed to have a positive lower bound. We first consider the Cauchy problem(the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is suffciently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave(weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.     

ON A PROBLEM OF(O,2)-INTERPOLATION

The object in this paper is to consider the problem of existence,uniqueness,explicil representation of(0,2)-interpolation on the zeros of(1-x~2)P~_(n-1)(x)/x when n is odd,where P_(n-1)denotes Legendrepolynomial of degree n-1,and the problem of convergence of interpolatory polynomials.     

TRIPLE SYMMETRIC POSITIVE SOLUTIONS TO NONLINEAR BVP WITH INTEGRAL BOUNDARY VALUE CONDITIONS

In the paper,we consider a nonlinear boundary value problem with integral boundary value conditions.By a generalization of the Leggett-Williams fixed-point theorem,we provide sufficient conditions for the existence of at least three positive solutions to the problem.An example is introduced to demonstrate our result.