SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRM SPACE-TIME

In this article, we concern the motion of relativistic membranes and null mem- branes in the Reissner-Nordstrom space-time. The equation of relativistic membranes moving in the Reissner-Nordstrom space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-NordstrSm space-time.

SYMMETRIC POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATIONS (AX,XB)=(C,D) AND AXB=C

The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.

Global Helically Symmetric Solutions to 3D MHD Equations

We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the three-dimensional magnetohydrodynamic equations in R3 when initial data are helically symmetric. Moreover, the large-time behavior of the strong solutions is obtained simultaneously.

EXISTENCE AND ITERATION OF POSITIVE SYMMETRIC SOLUTIONS TO A MULTI-POINT BOUNDARY VALUE PROBLEM

In this paper,we consider the existence of symmetric solutions to a nonlinear second order multi-point boundary value problem,and establish corresponding iterative schemes based on the monotone iterative method.

Existence and Asymptotic Behavior of Radially Symmetric Solutions to a Semilinear Hyperbolic System in Odd Space Dimensions

This paper is concerned with a class of semilinear hyperbolic systems in odd space dimensions. Our main aim is to prove the existence of a small amplitude solution which is asymptotic to the free solution as t →-∞ in the energy norm, and to show it has a free profile as t →＋∞. Our approach is based on the work of [11]. Namely we use a weighted L^∞ norm to get suitable a priori estimates. This can be done by restricting our attention to radially symmetric solutions. Corresponding initial value problem is also considered in an analogous framework. Besides, we give an extended result of [14] for three space dimensional case in Section 5, which is prepared independently of the other parts of the paper.

SOME EXACT SOLUTIONS OF 3-DIMENSIONAL ZERO-PRESSURE GAS DYNAMICS SYSTEM

The 3-dimensional zero-pressure gas dynamics system appears in the modeling for the large scale structure formation in the universe. The aim of this paper is to construct spherically symmetric solutions to the system. The radial component of the velocity and density satisfy a simpler one dimensional problem. First we construct explicit solutions of this one dimensional case with initial and boundary conditions. Then we get special radial solutions with different behaviours at the origin.

A class of exact solutions for N-dimensional incompressible magnetohydrodynamic equations

In this paper, a sufficient and necessary condition is presented for existence of a class of exact solutions to N-dimensional incompressible magnetohydrodynamic （MHD） equations. Such solutions can be explicitly expressed by appropriate formulae. Once the required matrices are chosen, solutions to the MHD equations axe directly constructed.

THE GENERAL SOLUTION ON NONLINEAR AXIAL SYMMETRICAL DEFORMATION OF NONHOMOGENEOUS CYLINDRICAL SHELLS

In this paper, the general solution on nonlinear axial symmetrical deformation of nonhomogeneous cylindrical shells is obtained by step reduction method[1]. The general formula of displacements and stress resultants, which is used to solve the bending problems of nonhomogeneous cylindrical shells under arbitrary axial symmetric loads, is derived. Its uniform convergence is proved. Finally, it is only necessary to solve one set of binary linear algebraic equations. A numerical example is given at the end of the paper which indicates satisfactory results of displacement and stress resultants can be obtained and converge to the exact solution.

MAXIMAL ATTRACTORS FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS OF VISCOUS AND HEAT CONDUCTIVE FLUID

This article is concerned with the existence of maximal attractors in Hi （i = 1, 2, 4） for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rn（n = 2,3）. One of the important features is that the metric spaces H（1）, H（2）, and H（4） we work with are three incomplete metric spaces, as can be seen from the constraints θ 〉 0 and u 〉 0, with θand u being absolute temperature and specific volume respectively. For any constants δ1, δ2……,δ8 verifying some conditions, a sequence of closed subspaces Hδ（4） H（i） （i = 1, 2, 4） is found, and the existence of maximal （universal） attractors in Hδ（i） （i = 1.2.4） is established.

Symmetric Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem

In this paper, we consider the following second order three-point boundary value problem u″（t）＋a（t）f（u（t））=0,0〈t〈1,u（0）-u（1）=0,u＇（0）-u＇（1）=u（1/2）,where a ： （0, 1） → [0, ∞） is symmetric on （0, 1） and may be singular at t = 0 and t = 1, f ： [0, ∞） → [O, ∞） is continuous. By using Krasnoselskii＇s fixed point theorem ia a cone, we get some existence results of positive solutions for the problem. The associated Green＇s function for the three-point boundary value problem is also given.

Symmetric Periodic Noncollision Solutions for N-Body-Type Problems

Using the calculus of variations in the large,especially computing the category of the symmetric configuration space of symmetric N-body-type problems,we prove the existence of infinitely many symmetric noncollision periodic solutions about the symmetric and nonau- tonomous N-body-type problems under the assumptions that the symmetric potentials satisfy the strong force condition of Gordon.

Three Symmetric Positive Solutions for Second-order Nonlocal Boundary Value Problems

Using the Leggett-Williams fixed point theorem, we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u″（t）＋g（t）f（t,u（t））=0,0〈t〈1,u（0）=u（1）=∫01m（s）u（s）ds. where m ∈ L1[0 1], g ： （0, 1）→ [0, ∞） is continuous, symmetric on （0, 1） and maybe singular at t = 0 and t = 1, f： [0, 1] × [0, ∞） → [0, ∞） is continuous and f（-, x） is symmetric on [0, 1] for all x∈ [0, ∞）.

Bubbling solutions of fourth order mean field equations on S^(4)

In this paper,we first establish the existence of blow-up solutions with two antipodal points of the fourth order mean field equations on S^(4).Moreover,we construct non-axially symmetric solutions with blow-up points at the vertices of regular configurations,i.e.,equilateral triangles on a great circle,regular tetrahedrons,cubes,octahedrons,icosahedrons and dodecahedrons.The bubbling rates of these blow-up solutions rely on various bubbling configurations.

THE SYMMETRIC POSITIVE SOLUTIONS OF 2n-ORDER BOUNDARY VALUE PROBLEMS ON TIME SCALES

In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.

Periodic Solutions of Prescribed Energy for a Class of Symmetric Singular Dynamical Systems

We consider the following Hamiltonian system: q″(t)+V′(q(t))=0 q ∈C^2(R,R^n\{0}) (HS) where V ∈C^2(R^n\{0},R)is an even function.By looking for closed geodesics,we prove that (HS)has a nonconstant periodic solution of prescribed energy under suitable assumptions.Our main assumption is related with the strong force condition of Gordon.

Three Solutions of p-Laplacian Equations Via a Critical Point Theorem of Ricceri

In this paper,we consider the following quasilinear diferential equation（p（u′））′＋λf（t,u）=0subject to one of the two boundary conditions：u（0）=u′（1）=0,u′（0）=u（1）=0.After transforming them into a problem of symmetrical solutions,the existence of three solutions of the problem is obtained by using a recent critical point theorem of Recceri.An example is given to demonstrate our main result.

Global Existence of the Radially Symmetric Strong Solution to Navier-Stokes-Poisson Equations for Isentropic Compressible Fluids

We prove the two existence results of the radially symmetric strong solutions to the Navier- Stokes-Poisson equations for isentropic compressible fluids. The important point in this paper is that the initial density is vacuum. It is different from weak solutions. Now we need some compatibility condition.

The explicit symmetry breaking solutions of the Kadomtsev-Petviashvili equation

To describe two correlated events,the Alice-Bob(AB)systems were constructed by Lou through the symmetry of the shifted parity,time reversal and charge conjugation.In this paper,the coupled AB system of the Kadomtsev-Petviashvili equation,which is a useful model in natural science,is established.By introducing an extended Backlund transformation and its bilinear formation,the symmetry breaking soliton,lump and breather solutions of this system are derived with the aid of some ansatze functions.Figures show these fascinating symmetry breaking structures of the explicit solutions.

Deformation Argument under PSP Condition and Applications

In this paper we introduce a new deformation argument,in which C^(0)-group action and a new ty pe of Palais Smale condition PSP play important roles.This type of deformation results are studied in[17,21]and has many different applications[10,11,17,21]et al.Typically it can be applied to nonlinear scalar field equations.We give a survey in an abstract functional setting.We also present another application to nonlinear elliptic problems in strip-like domains.Under conditions related to[5,6],we show the existence of infinitely many solutions.This ex tends the results in[8].

DIRICHLET BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER QUASI-LINEAR DIFFERENTIAL EQUATIONS WITH CHANGING SIGN NONLINEARITIES

This paper is concerned with the existence of positive solutions of two-point Dirichlet singular and nonsingular boundary problems for second-order quasi-linear differential equations with changing sign nonlinearities.