P-sets and Its Dependence Characteristic

P-sets is a set pair, it is composed of internal P-set and outer P-set, it has dynamic characteristic. By using structure of P-sets, dependence theorem and identification theorem are proposed in this paper.     

Growth Theorem and Distortion Theorem for a Sub class of Parab olic Starlike Mappings

In this article, we firstly introduce a subclass of parabolic starlike mappings writen as P S (β;ρ). Secondly, the growth theorem for P S (β;ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of P S (β;ρ), the distortion theorem along a unit direction is also established.     

One Kind of Mappings with Parametric Representation in Cn

In this paper, a kind of mappings with parametric representation is introduced, the growth theorem is set up.     

Cartan’s Second Main Theorem and Mason’s Theorem for Jackson Difference Operator

Let f : C → Pⁿ be a holomorphic curve of order zero. The authors establish a Jackson difference analogue of Cartan’s second main theorem for the Jackson q-Casorati determinant and introduce a truncated second main theorem of Jackson difference operator for holomorphic curves. In addition, a Jackson difference Mason’s theorem is proved by using a Jackson difference radical of a polynomial. Furthermore, they extend the Mason’s theorem for m + 1 polynomials. Some examples are constructed to show that their results are accurate.     

ON RUBIN’S HARMONIC ANALYSIS AND ITS RELATED POSITIVE DEFINITE FUNCTIONS

In this paper,a new formulation of the Rubin’s q-translation is given,which leads to a reliable q-harmonic analysis.Next,related q-positive definite functions are introduced and studied,and a Bochner’s theorem is proved.     

A Note on a Functional Differential Equation with State Dependent Argument

This paper is concerned with solutions of a functional differential equation.Using Krasnoselskii's fixed point theorem,the solutions can be obtained from periodic solutions of a companion equation.     

ON THE VALIRON’S THEOREM IN THE POLYDISK

In this paper, we discuss the Valiron's theorem in the unit polydisk DN. We prove that for a holomorphic map φ : DN→ DNsatisfying some regular conditions, there exists a holomorphic map θ : DN→ H and a constant α 0 such that θoφ =1/aθ.It is based on the extension of Julia-Wolff-Carath′eodory(JWC) theorem of D in the polydisk.     

一种新形式的二元混合有理插值(英文)

Newton＇s polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of bivariate blending rational interpolants.Characteristic theorem is discussed.We give some new blending interpolation formulae.     

A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.     

NEW RESULTS ON THE EXISTENCE OF PERIODIC SOLUTIONS TO LINARD EQUATION

In this paper, a Liénard equation with a deviating argument has been studied by means of Mawhin's continuation theorem. A new result guaranteeing the existence of periodic solutions is obtained.     

Positive solutions for quasilinear second order differential equation

It is well known that the Krasnoselskii's fixed point theorem is very very important. It was extensively used for studying the boundary value problems. In this article, the Krasnoselskii's fixed point theorem is extended. The new fixed point theorem is obtained. The second order quasilinear differential equation (Φ (y′))′+a(t)f(t,y,y′)=0,, 0<t<1 subject to mixed boundary condition is studied, where f is a nonnegative continuous function, Φ (v)= |v|^p-2 v, p>1. We show the existence of at least one positive solution by using the new fixed point theorem in cone.     

The existence of solutions of infinite boundary value problems for first-order impulsive differential systems in Banach spaces

In this paper, the existence of solutions of infinite boundary value problems for first-order impulsive differential systems is obtained by means of the Schauder fixed point theorem in a Banach space.     

Existence and multiplicity results for nonlinear nonautonomous second-order systems

In this paper we consider nonlinear periodic systems driven by the ordinary p$p$-Laplacian and having a nonsmooth potential function. Under minimal and natural hypotheses on the nonsmooth potential and using variational methods based on the nonsmooth critical point theory we prove four existence theorems and a multiplicity theorem. We conclude the paper with an existence theorem for the scalar problem, in which the energy functional is indefinite (i.e. it is unbounded both above and below).     

Doubly periodic solutions to a coupled telegraph system

While the nonlinearities are bounded below, we establish the existence and multiplicity results of doubly periodic solutions for a coupled nonlinear telegraph system with a parameter. The proof is based on a well known fixed theorem in a cone.     

Positive solutions for second-order four-point boundary value problems with alternating coefficient

In this paper, we investigate the existence of positive solutions for a class of nonlinear second-order four-point boundary value problems with alternating coefficient. Our approach relies on the Krasnosel’skii fixed point theorem. The result of this paper is new and extent the previously known result.     

Conditions for the existence of positive solutions covering a class of boundary value problems in a uniform way

In this paper, we will give conditions which will guarantee the existence of positive solutions for a variety of second order boundary value problems, using the well-known Krasnoselskii fixed point theorem. We will deal with a specific differential equation meeting a specific initial condition and use a general boundary condition, involving a not necessarily linear functional. Our purpose is to pose conditions on that functional, which will guarantee that the Krasnoselskii fixed point theorem can be applied. It is important to notice that only the values of this functional on two specific functions are involved in the conditions we pose. This paper unifies the way we deal with a wide variety of boundary value problems and provides results which, to the best of our knowledge, are new.     

The existence of countably many positive solutions for singular multipoint boundary value problems

In this paper, we study the existence of countably many positive solutions for a singular multipoint boundary value problem. By using fixed-point index theory and the Leggett-Williams’ fixed-point theorem, sufficient conditions for the existence of countably many positive solutions are established.     

Existence of doubly periodic solutions for a class of telegraph system with indefinite weight

Using the method of monotone iteration and Schauder fixed point theorem, we establish the existence of doubly periodic solutions for a coupled nonlinear telegraph system with indefinite weight.     

On the existence of positive solution for a kind of multi-point boundary value problem at resonance

This paper concerns the existence of positive solution for a class of second-order m-point boundary value problems under different resonant conditions. By using the Leggett-Williams norm-type theorem due to O’Regan and Zima, we obtain the existence of positive solution. An example is given to demonstrate the main results.     

Problems of periodic solutions for a type of Duffing equation with state-dependent delay

Sufficient criteria are established for the existence of periodic solutions to a type of Duffing equation with state-dependent delay, which improve and generalize some related results in the literature. The approach is based on Mawhin’s continuation theorem. The significance of the present paper is that our results are relevant to delay by Lemma 2.1, which is different from the corresponding results of past work.