A REMARK ON THE PERTURBATION OF CRITICAL MANIFOLDS

Given a C~2-function f on a Hilbedrt Riemannian manifold M, let ∑ be a. nondegonerate critical manifold of f, what becomes of ∑, if we perturbe f to f+g? When g is a C~2 perturbation, i.e. ||g||c~2 is small, there was a result due to M. Reeken by the inverse function theorem. It was rediscovered by Ambrosetti et.     

A REMARK ON GENERAL COMPLEX(α,β)METRICS

In this paper,we give a characterization for the general complex(α,β)metrics to be strongly convex.As an application,we show that the well-known complex Randers...     

A REMARK ON PERRON''''S METHOD IN THE PROOF OF THE PEANO THEOREM

The Perron method of major and minor functions has wide applications in analysis, in the theory of integral, in ordinary and partial differential equations, and in axiomatic potential theory. Peano's theorem states that the initial value problem     

ON THE SUFFICIENT CONDITION FOR A CONVEX DOMAIN TO CONTAIN ANOTHER IN R_(2n)

1IntroductionandSomeLemmasInplalle,tileclassicalresultsontilesufficielltcollditiolll'oradonlailltocontaillallotherareobtainedinH.Hadwiger's['t,]first.Renobtaillstileeqllivalentformwhichisllloresilllplein[1],i.e.,TheoremLetDoandDIbethedomainsboulldedbythes…     

BCKLUND TRANSFORMATION ON SURFACESWITH CONSTANT MEAN CURVATURE IN R~(2.1)

In this paper, the authors obtain the Backlund transformation on time-likesurfaces with constant mean curvature in R~(2,1). Using this transformation, families ofsurfaces with constant mean curvature from known ones can be constructed.     

A REMARK ON DUALITY FOR THE SUM OF CONVEX FUNCTIONS IN GENERAL BANACH SPACES

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＥｂｅａｒｅａｌＢａｎａｃｈｓｐａｃｅ，ｎｏｔｎｅｃｅｓａｒｉｌｙｒｅｆｌｅｘｉｖｅ．ＬｅｔΦ，Ψ：Ｅ→］－∞，∞］ｂｅｔｗｏｌｏｗｅｒｓｅｍｉｃｏｎｔｉｎｕｏｕｓｃｏｎｖｅｘｆｕｎｃｔｉｏｎｓ．Ｗｅｄｅｎｏｔｅ...     

A REMARK ON _1 SUBSPACES OF L_1 (μ,X)

ＡＲＥＭＡＲＫＯＮ　_1　ＳＵＢＳＰＡＣＥＳＯＦＬΦ_１（μ，Ｘ）ＤｉｎｇＧｕａｎｇｇｕｉ（定光桂）；ＨｕａｎｇＳｅｎｚｈｏｎｇ（黄森忠）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｋａｉＵｎｉｖｅｒｓｉｔｙ，Ｔｉａｎｊｉｎ３０００７１，...     

H~p(R~(n_1)×…×R~(n_m))空间的原子合成(0

朱学贤 《数学学报》1991,(2)

POSITIVE SOLUTIONS FOR NONHOMOGENEOUS ELLIPTIC EQUATIONSWITH CRITICAL GROWTH ON R~(2)

1IntroductionIntillspaper,weare(follccrlledwitlltileexistellccofPositly(tsollltiollsoftilefollowillgnonhonlogelleousellipticProblclll:whereg(x)EL'(R'),g(:v)Z0alldg(x)t0,f(x,t)=h(x,t).hi=withb>0,h(x,t)EC(R=xR,R)alldtilefollowing(CI)-(C3)11old:(CI)sliphillM0.linljfl- x,h(T,t)(t--if-=011llif'orllllyforxeR2.hill}t:l-:,t)(axle(~ltJ')= lx,11lliforllllyl'Ora:6RZ.ltl~la(C3)ThereexistM>0,aE(0,1]sucllthatFOllowing[1,5],wesaythatf(x,t)=h(x,f…     

H~p(R~(n_1)×…×R~(n_m))空间的原子合成(0

朱学贤 《数学学报》1991,34(2):213-221

MULTIPLICITY OF PERIODIC SOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION MULTIPLICITY OF PERIODIC SOLUTIONS OF DUFFING'S EQUATIONS WITH LIPSCHITZIAN CONDITION

1. IntroductionWe deal with the Duffing equationi g(x) ~ p(t), (1.1)where g(x), p(t) E C(R, R) and p(t) is periodic, whose least period is 27. The multiplicityof periodic solutions of Equation (l.1) has been widely studied since the 50s. In [1], T.Ding studied the multiplicity of periodic solutions of Equation (1.1) under the followingconditions.(gi) Let g(x) E C'(R, R), and let K be a positive constant, such that(gi) There exist two constallts Ac > 0 and MO > 0 such thatg(x) w~ > AO…     

PERIODIC SOLUTIONS OF LINEAR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS

Consider the linear neutral FDEd/dt[x(t) Ax(t - r)] = R [dL(s)]x(t s) f(t)where x and / are ra-dimensional vectors; A is an n x n constant matrix and L(s) is an n x n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.     

HARNACK ESTIMATES FOR WEAK SOLUTIONS OF EQUATIONS OF NON-NEWTONIAN POLYTROPIC FILTRATION

51. IntroductionIn this paper we investigate the local behavior of nonnegative weak solutions for theequations of non-Newtonian polytropic filtrationac -- div(IDumlp--'Dam) = 0,m(p -- 1) < 1,m > 0,p > l, in D'(flT),u E CI..(0, T; L?o.(n)), urn E Lro.(0, T; WI:)l(fl)), (1.1)where n is an open set of R", N 2 1, 0 < T < ool fiT ~ fix (0, T), and D ~ (k,', e).Equation (1.1) appears in a number of applications to describe the evolution of diffusion.The evolution HLaplacian equationut ~ …     

具有无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程的周期解问题.利用矩阵测度和Krasnoselskii不动点定理得到了周期解的存在性和唯一性定理;特别地,当Q（s）为零矩阵,A（t,x）=A（t）时给出了存在唯一稳定的周期解的条件.     

不稳定型二阶中立型方程正解的存在性与有界振动

本文研究一类不稳定型二阶中立型微分方程正解的存在性与有界振动．证明了在一定条件下不稳定型二阶中立型方程总存在无界正解，并给出了保证其方程的一切有界解都振动的充分条件，改进了文［１，２］中的有关条件．     

TWO EXISTENCE THEOREMS OF PERIODIC SOLUTIONS FOR DIFFERENTIAL DELAY EQUATIONS

ＴＷＯＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＤＩＦＦＥＲＥＮＴＩＡＬＤＥＬＡＹＥＱＵＡＴＩＯＮＳ￥ＧＥＷＥＩＧＡＯＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｃｏｒｒｅｃｔｓａｎｄｉｍｐｒｏｖｅｓｔｗｏｔｈｅｏｒｅｍｓ...     

MULTIPLICITY OF PERIODIC SOLUTIONS OF DUFFING’S EQUATIONS WITH LIPSCHITZIAN CONDITION

This paper deals with the existence and multiplicity of periodic solutions of Duffing equations . The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided thatg(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.     

广义 Liénard方程周期解的存在性和不存在性

研究了广义 Ｌｉéｎａｒｄ方程ｘ＋ｆ（ｘ,ｘ）ｘ＋ｇ（ｘ）＝ ０周期解的存在性和不存在性,在一定条件下,我们得到了非零周期解的存在与不存在的一些充分条件．     

DIRECT CONSTRUCT OF PERIODIC SOLUTIONS TO PERTURBED KLEIN-GORDON EQUATIONS BY NEWTON ITERATION

61. IntroductionNear an equilibrium state to a system of nonlinear ODEs, one can regard the nonlinearsystem as a perturbation of its linearization. It is well known that if none of the characteristicexponents of the linearized system has zero real part, then the phase portrait near theequilibrium of the nonlinear system is topologically equivalent to that of its linearization(cL [181). However, if characteristic exponents with zero real part appearl then the linearizedsystem alone does not c…     

STABILITY AND EXISTENCE OF PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS ON LIENARD SYSTEMS

1MainResultsConsidersystem11~.x f(x)x' g(x)~0(1)wheref(x)islocallyintegrable,g(x)isdifferentiablealldg(0)=0.Theroem1Thezerosolutionofsystem(1)isuniformlyasymptoticallystableifbyequivalenttransf'Ormu=xov=X' F(x).DefineW[t,(uif\v)]j6ug(s)ds Iv',thenwisaposi…