SOME BOUNDARY PROBLEMS OF THE SPIN SYSTEMS AND THE SYSTEMS OF FERRO-MAGNETIC CHAIN Ⅱ. Mixed Problems and Others

In the present paper the authors considered the mixed problem with nonlinear boundary conditions and the initial condition for the spin system and the system of ferro-magnetic chain in the rectangular domain Q_t.     

BOUNDARY VALUE PROBLEMS FOR THE EQUILIBRIUM SYSTEMS OF FERRO-MAGNETIC CHAIN

ＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＴＨＥＥＱＵＩＬＩＢＲＩＵＭＳＹＳＴＥＭＳＯＦＦＥＲＲＯ－ＭＡＧＮＥＴＩＣＣＨＡＩＮＳｈｅｎＹａｏｔｉａｎ（沈尧天）ＹａｎＳｈｕｓｅｎ（严树森）（Ｄｅｐｔ：ｏｆＡｐｐｌ．Ｍａｔｈ，ＳｏｕｔｈＣｈｉｎａＵ...     

ON THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

§ 1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space W_t~2~(1,2)(O, +∞) into L_t~2~q(O, ∞), v>2. When v=N-1 we can get the radial solutions of problem where 2~*=2N/N-2 is the critical exponent of the Sobolev embedding H~1(R~n)→L~Q(R~N). Kurtz has discussed the existence of κ-node solution of (1.1), (1.2) for each κ∈N U{0} when the growth rate of |u|~(l-1)u+f(u) is lower then |u|~(v+3/v-1) i.e.     

ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper we prove the existence of k-node solution of singular nonlinear boundary value problems for each k∈N ∪ {0}.     

THE COMPARISON OF ASYMPTOTIC BEHAVIOR OF THE SOLUTION OF EQUIVALUED BOUNDARY VALUE PROBLEMS FOR NONLINEAR AND LINEAR ELLIPTIC EQUATIONS

This paper shows the different asymptotic behavior of the solution of equivalued boun-dary value problems for nonlinear equation from the solution to linear one,while the boundary,on which the equivalued boundary value is carried,shrinks to afixed point.     

SOME ESTIMATIONS OF SOLUTION OF NONLINEAR BOUNDARY VALUE PROBLEM FOR SECOND ORDER SYSTEMS

We study the nonlinear boundary value problem: where ε>0 is a small paramete, y, f, A and B are n-dimensional vector functions. This vector nonlinear bundary value problem does not appear to have been studied, although the scalar boundary value problem has been treated extensively. Under appropriate assumptions, using method of differential inequality we can find a solution and estimate it as well.     

SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem.Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension,the existence of solutions of the above problem is proved.In this article,the complex analytic method is used,namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed,afterwards the above problem for the degenerate elliptic equations of second order is solved.     

BOUNDARY VXLUE PROBLEMS FOR SYSTEMS OF NONLINEAR SECOND ORDER DIFFERENTIAL DFFERENCE EQUATIONS

ＢＯＵＮＤＡＲＹＶＸＬＵＥＰＲＯＢＬＥＭＳＦＯＲＳＹＳＴＥＭＳＯＦＮＯＮＬＩＮＥＡＲＳＥＣＯＮＤＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＤＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＳ￥ＭＩＡＯＳＨＵＭＥＩＡｂｓｔｒａｃｔ：Ｔｈｅａｕｔｈｏｒｓｔｕｄｉｅｓｔｈｅｂｏｕ...     

OSCILLATION OF SOLUTIONS OF THE SYSTEMS OF QUASILINEAR HYPERBOLIC EQUATION UNDER NONLINEAR BOUNDARY CONDITION

Sufficient conditions are obtained for the oscillation of solutions of the systems of quasilinear hyperbolic differential equation with deviating arguments under nonlinear boundary condition.     

EXISTENCE OF FORECAST AND DECISION HORIZONS FOR OPTIMAL CONTROL PROBLEMS OF NONLINEAR SYSTEMS

ＥＸＩＳＴＥＮＣＥＯＦＦＯＲＥＣＡＳＴＡＮＤＤＥＣＩＳＩＯＮＨＯＲＩＺＯＮＳＦＯＲＯＰＴＩＭＡＬＣＯＮＴＲＯＬＰＲＯＢＬＥＭＳＯＦＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＳ￥ＺｈａｎｇＣｈｅｎｇｙｕｎ（张成云）（ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，复旦大学，邮编：...     

THE BOUNDARY VALUE PROBLEMS FOR THE HIGHER ORDER QUASILINEAR PARABOLIC AND ELLIPTIC SYSTEMS SATISFYING GENERAL BOUNDARY CONDITIONS

In this paper, the existence and uniqueness of the boundary value problems for the higher order quasilinear parabolic systems satisfying general boundary conditions and initial value condition are considered. We have concluded the problems to the following: if all the solutions of a family of problems of the same type which are derived from a substitution of τf(s, t, u, ...,Dx~(2b-1)u), τgj(y, t, u) and τ(x) (0≤τ≤1) for f, g, and φ respectively are uniformly bounded, then the original problems have a unique solution in H~(2b a,1 a/2b)((?)_T). Under assumption that the linear problems have a unique solution, we have proved the existence and uniqueness of the solution of the boundary value problems for the quasillnear elliptic systems.     

EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS

This paper is concerned with the following second-order vector boundary value problem ：x^R=f（t,Sx,x,x＇）,0〈t〈1,x（0）=A,g（x（1）,x＇（1））=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.     

EXISTENCE OF SOLUTIONS OF NONLINEAR TWO AND THREE-POINT BOUNDARY VALUE PROBLEMS FOR FOURTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, the two and three-point boundsry problems (with nonlinear boundary conditions)for the genaral noniinear equations of fourth order are discussed.We have set some grups of the assurnpion coditions and proved the existence of solutins for corresponding boundary value problems under these conditons.     

THE EXISTENCE OF INFINITELY MANY SOLUTIONS OF NONLOCAL BOUNDARY VALUE PROBLEMS FOR NONLINEAR ELLIPTIC EQUATIONS

Let Ω be a bounded domain in R~n with smooth boundary, a uniformly elliptio and self-adjoint operator, whose coefficients are real and smooth; M an arbitrary close subspace ia H~(1/2)((?)Ω), and     

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR HIGHER ORDER NONLINEAR THREE-POINT BOUNDARY VALUE PROBLEMS

In this paper,by using Leray-Schauder degree theory,we establish the exi- stence and uniqueness theorems for some higher order nonlinear three-point boundary value problems.     

GLOBAL EXISTENCE OF THE SOLUTION FOR THE LANDAU-LIFSHITZ EQUATION OF THE FERROMAGNETIC SPIN CHAIN

1IntroductionInthepresentpaper,wecollsidertileLandau-LifSllitzequationoftileferromagneticspinchainwhichtakestheform:where"x'ldenotesthevectorcrossproductinR',fi=(--D,D),D>0,u=(ul,u3,u3):fixR -R3istilespinvector,or>0isaGilbertdampingconstant,Pisarealparameter,J=diag(ri,acfac)isaconstantmatrix.TheaboveequationarisesinthedoublyanisotropicHeisenbergspinsystem.Thissystemisimpliedbytileconservationofenergyandmagnitudeofu.SeeDanielandLab.hmanan[1]please.Insomeferromagneticchainsystems,thematri…     

LIMIT CYCLES AND CENTER-FOCUS OF NONLINEAR SYSTEMS

The authors consider the nonhnear systems x=h(y)-F(x),y=-g(x) in which g(x) may be not differentiabte and the system can be nonsymmetric. Some conditions which en-sure that there exists an infinite number of limit cycles are obtained. A problem about center-focus put forward by R. Conti has been answered.     

POSITIVE SOLUTIONS OF NONLINEAR FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS

By constructing a special cone and using the fixed point theorem of cone expansion and compression,this paper investigates fourth-order singular boun- dary value problems with sublinear effect and presents some necessary and sufficient conditions for existence of C~2 or C~3 positive solutions.Further,some examples are given concerning the applications of our main results.     

NONLINEAR BOUNDARY PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

By means of the supersolution and subsolution method and monotone iteration technique, the following nonlinear elliptic boundary problem with the nonlocal boundary conditions is considerd. The sufficient conditions which ensure at least one solution are given. Furthermore, the estimate of the first nonzero eigenvalue for the following linear eigenproblem is obtained, that is λ_1≥2α/(nd~2).     

THE STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL SYSTEMS

In this paper, the author uses the methed of inequality analysis to study the stability of nonlinearneutral differential systems. Some criteria for being exponentially stable in the large in C_1 space areobtained.