ON LEVIN TYPE COMPARISON THEOREMS FOR CERTAIN SECOND ORDER DIFFERENTIAL EQUATIONS

1IntroductionIn1960,A.Ju.Levint12]provedthefonowingcomparisontheorem.Theorem1Letu(t)andv(t)besolutionsofrespectivelysuchthatu(f)f0fortEIap,P],v(cr)/0andtheinequalityholdsforalltE[or,p],wherep,qEC[a,P].Then,foralltE[o,0],v(t)/0andSincetheappearanceOfLevin'sfundamentalpaper[12],anumberofpapershaveaampearedintheliteraturewhichdealswithvariousgeneralizationsandextensionsofTheoremL,see[l,5,8-11,14,16].ThemainpurposeofthispaperistoestablishdeferentialequationsOftheforms:where(n)a,bEC'(I,(0,…     

ON CERTAIN BOUNDARY VALUE PROBLEMS FOR NONLINEAR INTEGRODIFFERENTIAL EQUATIONS

ＯＮＣＥＲＴＡＩＮＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＮＯＮＬＩＮＥＡＲＩＮＴＥＧＲＯＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＤ．Ｇ．Ｐａｃｈｐａｔｔｅ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＳｔａｔｉｓｉｃｓＭａｒａｔｈ...     

GLOBAL EXISTENCE FOR NONLINEAR PARABOLIC EQUATIONS

This paper is concerned with the global existence of Cauchy problem for nonlinearparabolic equations.The sharp results concerning the space dimension have been obtainedwhich improve the corresponding results obtained by S.Klainerman.     

ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS

0IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblemforthefailliliarequationwherefiisaboundeddomaininR"withsmoothboulldaryoff,p22isacollstantalldlp(z,u)l5of'(tl" 'forsomea20andc>0.FOrp(x,ti)=Itll"'u,theauthorsofpaper[4,7llolwereillterestedillllollllegativesolutionandhadobtainedfollowillgresults(alsosee[12]).1)If25a 2相似文献   

GLOBAL ATTRACTOR FOR CAMASSA-HOLM TYPE EQUATIONS WITH DISSIPATIVE TERM

1IntroductionWe consider the Camassa-Holm type equations with dissipative termut?uxxt δuxxxx f(u)x=ε(2uxuxx uuxxx) g(x),x∈[0,1],t>0.(1.1)Under nonlinear boundary conditionu(0,t)=ux(1,t)=uxx(0,t)=0,t>0,(1.2)δuxxx(1,t)?εu(1,t)uxx(1,t)=?(u(1,t)),t>0,(1.     

TWO EXISTENCE THEOREMS OF PERIODIC SOLUTIONS FOR DIFFERENTIAL DELAY EQUATIONS

ＴＷＯＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＤＩＦＦＥＲＥＮＴＩＡＬＤＥＬＡＹＥＱＵＡＴＩＯＮＳ￥ＧＥＷＥＩＧＡＯＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｃｏｒｒｅｃｔｓａｎｄｉｍｐｒｏｖｅｓｔｗｏｔｈｅｏｒｅｍｓ...     

EXISTENCE THEOREMS FOR RANDOM MEASURES

Two existence theorems of random measures on a separable complete metric space areproved.It seems that the theory of random measures in locally compact spaces and that inseparable complete metric spaces are essentially different by noting that the critera fortightness of the locally finite measures is much more tedious than that of the Radommeasures.     

ON OSCILLATION THEOREMS. FOR HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper,we investigate the complex oscillation of the differential equation f^(k) Ak-1f^(k-1)… A1f^1 A0f=F(x) where Af(j=0,…,k-1)F 0 are finite order entire functions. And we give precise estimates of the exponent of convergence of the zero-sequence of solutions for the above equation under some additional hypotheses.     

EXISTENCE AND UNIQUENESS OF GLOBAL SOLUTION FOR CERTAIN NONLINEAR DEGENERATE PARABOLIC SYSTEMS

ＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＧＬＯＢＡＬＳＯＬＵＴＩＯＮＦＯＲＣＥＲＴＡＩＮＮＯＮＬＩＮＥＡＲＤＥＧＥＮＥＲＡＴＥＰＡＲＡＢＯＬＩＣ　ＳＹＳＴＥＭＳＬＵＧＵＯＦＵ（卢国富）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｐｕｔｉ...     

ON THE EXISTENCE AND UNIQUENESS OF CLASSICAL GLOBAL SOLUTION TO A TYPE OF B0USSINESQ EQUATIONS

The existence and uniqueness of classical global solutions to a type of Boussinesq equations withinitial and boundary values are studied in this paper. The existence of such solutions is proved bymeans of compactness theorem and Schauders fixed point theorem, and its uniqueness by the so calledenergy method.     

GLOBAL EXISTENCE FOR A CLASS OF SYSTEMSOF NONLINEAR WAVE EQUATIONS INTHREE SPACE DIMENSIONS

Consider a system of nonlinear wave equationsfor i = 1, … , m, where F, (i = 1, … , m) are smooth functions of degree 2 near the origin of their arguments, and u = (u1, … ,um), while u and x u represent the first and second derivatives of u, respectively. In this paper, the author presents a new class of nonlineaxity for which the global existence of small solutions is ensured. For example, global existence of small solutions for arbitrary cubic terms,arbitrary cubic termswill be established, provided that c12 ≠ c22.     

ON SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper, using the theory of resolvent operators, Banach,s contraction prin-ciple and Schauder,s fixed point theorem, we study the existence of integral solutions to semilinear integrodifferential equations under nonlocal conditions in Banach space. An example is provided to illustrate the results obtained.     

NOTES ON THE OSCILLATION FOR CERTAIN HYPERBOLIC EQUATIONS OF NEUTRAL TYPE

1IntroductionOwingtotheapplicationsinthefieldofnaturalscience,therehasbeenan.-.increasinginterestinoscillationtheoryofhyperbolicpartialfuncti0naldiffe-rentialequations['-']-Forexample,K.Kreith,T.KusonoandN.Yosidain[1],ChenandYuin[2]concernedthefollowingequations,respectivelyWen0tethatthoseworkshavebeenc0ncernedwith0nlythecase0fdiscretedeviatingarguments,theresultsoftheequationswithcontinu0usdeviatingargumentsareverylittle.Weknowonly0ntheworksofaclassof0rdinarydifferentialequations[5],parab…     

GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR GENERALIZED POCHHAMMER-CHREE EQUATIONS

In this article,we study the initial boundary value problem of generalized Pochhammer-Chree equation u_(tt)-u_(xx)-u_(xxt)-u_(xxtt)=f(u) xx,x ∈Ω,t 0,u(x,0) = u0(x),u t(x,0)=u1(x),x ∈Ω,u(0,t) = u(1,t) = 0,t≥0,where Ω=(0,1).First,we obtain the existence of local W k,p solutions.Then,we prove that,if f(s) ∈ΩC k+1(R) is nondecreasing,f(0) = 0 and |f(u)|≤C1|u| u 0 f(s)ds+C2,u 0(x),u 1(x) ∈ΩW k,p(Ω) ∩ W 1,p 0(Ω),k ≥ 1,1 p ≤∞,then for any T 0 the problem admits a unique solution u(x,t) ∈ W 2,∞(0,T;W k,p(Ω) ∩ W 1,p 0(Ω)).Finally,the finite time blow-up of solutions and global W k,p solution of generalized IMBq equations are discussed.     

SOME NEW RESULTS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF MIXED TYPE INTEGRODIFFERENTIAL EQUATION

In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u" = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper and lower solution method.     

Banach空间中混合单调脉冲微分-积分方程解的存在性

本文给出了Banach空间中混合单调脉冲微分-积分方程解、耦合最小最大解的存在性定理及单调迭代方法,改进和推广了[1]-[4]的相应结果．     

GLOBAL EXISTENCE FOR SEMILINEAR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

This paper is concerned with the global existence of solutions for abstract retarded functional differential equations (RFDEs) with infinite delay,via a fixed point approach.Some sufficient conditions are established under which the existence of a globally mild solution are obtained by using Leray-Schauder.     

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR THE 3D COMPRESSIBLE NON–ISENTROPIC EULER EQUATIONS WITH DAMPING

We investigate the global existence and asymptotic behavior of classical solutions for the 3D compressible non-isentropic damped Euler equations on a periodic domain. The global existence and uniqueness of classical solutions are obtained when the initial data is near an equilibrium. Furthermore, the exponential convergence rates of the pressure and velocity are also proved by delicate energy methods.