ON THE EXISTENCE OF POSITIVE SOLUTIONS TO SECOND ORDER PERIODIC BVPS

The existence of positive solutions to second-order periodic BVPs-u'+Mu =j(t, u),t(0) = u(2π),u'(0) = '(2π) and u'+ Mu = I(t, u), u(0) = u(2π), u'(0) = u'(2π)is proved by a simple appliCation of a Fixed point Theorem in cones due to Krasnoselskii.

Extended tanh-function Method for Solving Traveling Wave Solutions of Nonlinear Kundu Equation

In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′（t） ＋ p（t）x′（t） ＋ q（t）x（t） = f（t, x（t））.By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.

POSITIVE SOLUTIONS FOR SOME 1-DIMENSIONAL BOUNDARY VALUE PROBLEMS OF LAPLACE-TYPE

This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.

A THREE-DIMENSIONAL SOLUTION OF THE PROBLEM OF THREE FIXED CENTRES

Based on the definitions of three fixed centres in a four-dimensional space, a three-dimensional solution of the problem of three fixed centres is presented,whichdevelops the plane solution of the problem.

ZTE's Fixed Access Network Solution

This article introduces the Fiber-to-the-World total solution, a fixed access network solution launched by ZTE Corporation. The ZXA10-MSAN system, an important part of the solution, is presented. The ZXMSG 5200/5600 access gateway system, the updated version of ZXA10-MSAN, is also described. Moreover, ZXPON, the passive optical network system, is mentioned. The wide application of the solution is demonstrated by three application cases in the end.

Solutions to Convergence of Mobile and Fixed NGNs

NGN is the current hot topic of the fixed network development,while 3G is the trend of the mobile communication in the next few years. Since the emerging all-service operators will soon have new de- mands on communication network technologies,it is foreseeable that mobile and fixed NGNs converge.The article mainly analyzes the solutions to the convergence of mobile and fixed NGNs,and points out that convergence is a long-term goal.

On Skew Triangular Matrix Rings

In this paper, we prove the existence and uniqueness of positive solutions for a system of multi-order fractional differential equations. The system is used to represent constitutive relation for viscoelastic model of fractional differential equations. Our results are based on the fixed point theorems of increasing operator and the cone theory, some illustrative examples are also presented.

Controllability of Nonlinear Neutral Evolution Equations with Nonlocal Conditions

In this paper, we establish sufficient conditions for the controllability of nonlinear neutral evolution equations with nonlocal conditions. The result is obtained by using Krasnoselski-Schaefer type fixed point theorem.

Existence of Positive Solutions for Systems of Nonlinear Second-Order Differential Equations on the Half Line in a Banach Space

In this paper, the cone theory and MSnch fixed point theorem combined with the monotone iterative technique are used to investigate the positive solutions for a class of systems of nonlinear singular differential equations with multi-point boundary value conditions on the half line in a Banach space. The conditions for the existence of positive solutions are formulated. In addition, an explicit iterative approximation of the solution is also derived.

FIXED POINTS AND EXPONENTIAL STABILITY OF ALMOST PERIODIC MILD SOLUTIONS TO STOCHASTIC VOLTERRA-LEVIN EQUATIONS

In this paper, we consider stochastic Volterra-Levin equations. Based on semigroup of operators and fixed point method, under some suitable assumptions to ensure the existence and stability of pth-mean almost periodic mild solutions to the system.