EXISTENCE AND NONEXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS

In this paper an existence theorem of positive radial solutions to a class of semilinear elliptic systems is proved by the Leray-Schauder degree theorem. Also, a nonexistence theorem is obtained. As an application of the main theorem, an example is given.     

POSITIVE SOLUTIONS FOR DIRICHLET PROBLEMS OF SINGULAR SEMILINEAR ELLIPTIC EQUATIONS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＤＩＲＩＣＨＬＥＴＰＲＯＢＬＥＭＳＯＦＳＩＮＧＵＬＡＲＳＥＭＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＣＵＩＳｈａｎｇｂｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓ...     

QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS NONLINEARITIES

1.IntroductionInthispaperweshallconsideradiscontinuousnonlinearnonmonotoneellipticboundaryvalueproblem,i.e.aquasilinearelliptichemivariationalinequalitywhereAn=--Z:=,hat(x,u,7u) ac(x,usac)an4thesymbolaldesignatesclarke'sgeneralizedgradientofalocallyL...     

POSITIVE SOLUTIONS OF SINGULAR SUBLINEAR SECOND ORDER BOUNDARY VALUE PROBLEMS

1.IntroductionBoundaryvaluepr0blemsconcerningthegeneralizedEmden-F0wlerequationsx p(t)x'=O,(1)wherep(t)eC(O,1),p(t)20f0rtE(O,1),AER,havebeenstudiedbymanyauthors(see[1-51andthereferencestherein).InthispaperwetreattheDirichletproblem(1)withax(0)-bx'(0)=O,c…     

AN EXISTENCE THEOREM FOR RADIAL POSITIVE SOLUTIONS OF NONLINEAR DEGENERATE ELLIPTIC EQUATIONS

ＡＮＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＦＯＲＲＡＤＩＡＬＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＤＥＧＥＮＥＲＡＴＥＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＬＩＵＨａｉｌｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｎａｎＮｏ...     

NONTRIVIAL PERIODIC SOLUTIONS OF A SEMILINEAR WAVE EQUATION WITHOUT ASSUMPTION OF MONOTONICITY

In references,some authors have succeeded in obtaining existence re-sults of the superlinear wave equation without the assumption of monotonicity forthe nonlinear term.In this paper,we present existence results for this problem byusing local linking idea and improve some previous results.     

UPPER AND LOWER SOLUTIONS METHODS FOR EXISTENCE OF PERIODIC SOLUTIONS OF DUFFING EQUATION

1.IntroductionandNotationsInthispapertwestudytheexistenceofsolutionstothefollowingperiodicboundaryvalueproblemforthesecondorderDuffingequationwheresisarealparameter,g:[0,TIxR~RisaCarath6odoryfunctionandkER\{0}.Werecall(forexample,see[1])thatg:[0,TIxR~RiscalledaCarath6odoryfunctionifg(.,x)ismeasurableforallxERandg(t,.)iscontinuousfora.e.tE[0,TI.Theexistenceproblemfor(1.1)--(1.2)byusingtheupperandlowersolutionsmethodhasbeenstudiedbyFabryetal.in[2]foramoregeneralcasewhereacontinuousdampin…     

THE EXISTENCE OF SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN OPERATOR IN L^s-SPACES

By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s （Ω） of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈＋∞, and 2N/N＋1 〈 p ≤ 2 for N（≥ 1） which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.     

EXISTENCE OF MULTIPLE SOLUTIONS AND BIFURCATIONFOR CRITICAL SEMILINEAR BIHARMONIC EQUATIONS

ＥＸＩＳＴＥＮＣＥＯＦＭＵＬＴＩＰＬＥＳＯＬＵＴＩＯＮＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＦＯＲＣＲＩＴＩＣＡＬＳＥＭＩＬＩＮＥＡＲＢＩＨＡＲＭＯＮＩＣＥＱＵＡＴＩＯＮＳＥＸＩＳＴＥＮＣＥＯＦＭＵＬＴＩＰＬＥＳＯＬＵＴＩＯＮＳＡＮＤＢＩＦＵＲＣＡＴＩＯＮＦ...     

THE SINGULAR PERTURBATION OF NONLOCAL BOUNDARY VALUE PROBLEMS FOR NONLINEAR ELLIPTIC EQUATION OF FOURTH ORDER

Chenandothersstudiedaclassofsingularlyperturbedboundaryproblems[1--3].NowweconsiderthefollowingsingUlarlyperturbednonlocalboundaryvalueproblemforthenonlinearellipticequationoffourthorder.whereEisapositiveparameter,bistheLaplacian,ndenotesaboundedregi...     

UNIQUENESS OF THE POSITIVE SOLUTION FOR SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

This paper is concerned with the bounded value problems1/p(t)(p(t)u')'+f(u)=0, t>0, u'(0)=0, lim t→+∞ u(t)=0,where f(0)=0. Such problems arise in the study of semi-linear elliptic differential equa-tions in R~n. It is shown that the problem has at most one positive solution under appro-priate conditions on f and p. Our result can include the important case that p(t)=f~(n-1)and f(u)=u~P-u, where n>1, p>1 are some given constants.     

EXISTENCE OF THE VALUE FOR A DIFFERENTIAL GAME WITH SWITCHING STRATEGIES IN A BANACH SPACE

A two-player zero-sum differential game in some Banach space is studied.Positiveswitching costs are associated with each player.By regularizing the game and combining thenotion of viscosity solutions for Isaacs-Bellman equation,we obtain the existence of the Elliot-Kalton value of the game under suitable conditions.     

ASYMPTOTIC BEHAVIOR OF THE SOLUTION FOR THE NEUTRON TRANSPORT EQUATION IN A SLAB WITH GENERALIZED REFLECTING BOUNDARY CONDITIONS

This paper discusses the neutron transport equation in a slab with generalized reflectingboundary conditions.By means of the positive C_0-semigroup theory,we have proved that this problemhas a unique nonnegative solution and found the spectral property of the corresponding transportoperator.Finally we give the asymptotic behavior of the solution for this equation.     

SOLITON AND ELLIPTICAL PERIODIC SOLUTIONS TO THE MODIFIED NONLINEAR SCHRODINGER EQUATION

1.IntroductionAsiswellknown,theNLSE.02 ac Iql:q=0(1)'N Zap Iql:q=0(1)describesthepropagationofpicosecondOPticalpulseinamonomodeOPticalfiber,whereq(',T)istocomplexpulse,'represelltsthedistancealongthedirectionofpropagation,Trepresentsthetimeinthegroupvelocityframeandrs=11.TheNLSEhasbrightsolitonsolutionwhend==1,anddarksolitonsolutionwhena=11.Inthisnotewehaveobtainedthedarksolitonsolutionwhena~1.However,recentworkshaveshownthattheNLSEisnotsufficieDttodescribethepropagationoffemtosecond…     

ON THE BOUNDARY STABILIZATION OF WAVE EQUATION WITH VARIABLE COEFFICIENT

1.IntroductionLetfibeaboundedopendomaininR"(n22)withsmoothboundaryr,u~u(s)betheoutwordnormalofrats.GivenavectorxoER",denotem(x)gx--xo(x6R"),Rgsup{lm(x)fjxCfi}.SetLndsupposer nrAI~0.Weconsiderthefollowingwaveequationonfiwithboundaryfeedback:whereK=(m'u)k,L…     

A LIOUVILLE THEOREM FOR GLOBAL SOLUTIONS OF HOMOGENEOUS CAUCHY PROBLEM OF MRABOLIC EQUATIONS

ＡＬＩＯＵＶＩＬＬＥＴＨＥＯＲＥＭＦＯＲＧＬＯＢＡＬＳＯＬＵＴＩＯＮＳＯＦＨＯＭＯＧＥＮＥＯＵＳＣＡＵＣＨＹＰＲＯＢＬＥＭＯＦＭＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳ￥ＭＩＮＴａｉｓｈａｎ（ＢｅｉｊｉｎｇＬｉｇｈｔＩｎｄｕｓｔｒｙＩｎｓｔｉｔｕｔｅ，Ｂｅｉ...     

ON THE EXISTENCE OF MEROMORPHIC SOLUTIONS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＭＥＲＯＭＯＲＰＨＩＣＳＯＬＵＴＩＯＮＳＯＦＡＬＧＥＢＲＡＩＣＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳ￥ＹＵＡＮＷｅｎｊｕｎ（ＤｅｐａｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＮｏｏｒｍａｌＵｎｉｖｅｒｓ...     

GLOBAL CLASSICAL SOLUTIONS AND EXPLICITEXACT SOLUTIONS TO A KIND OF QUASILINEARPARTIAL DIFFERENTIAL EQUATIONS

1.IntroductionandMainResultTherearemanyexamplesconcerningtheformationofsingularitiesinthesoluti0nsofnon-linearpartialdifferefitialequations.Thus,althoughasolutionmaybesmoothinitially,itmaybecomesingularatsomelatertime(see[1-6]).However,T.Nishidahaspr0vedthatiftheCln0rmoftheinitialdataissufficientlysmall,thentheCauchyproblemadmitsauniqueglobalsmooths0lutionont2Otoareduciblequasilinearhyperbolicsystemwithfirst(lower)orderdissipativeterm(see[7]).Thereafter,manyauthorshavegeneralizedNishida'sr…     

ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS

In this paper,we use the contraction principle and the Leray-Schauder principleto deal with the existence of periodic solutions of the Volterra integral differential equation.Some new existence criteria and unique existence criteria are obtained.     

ON THE BOUNDEDNESS OF SOLUTIONS,EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF CUBIC DIFFERENTIAL SYSTEM

In this paper, we discuss the boundedness of the solutions, the existence andthe uniqueness of the limit cycle of the following cubic differential system:x'=y, y'=-x+δy+a_2xy+a_4x+a_5x~2y. (*)We obtain the following results:(1) System (*) is bounded if and only if (i) a_5<0, a_4=0; or (ii) a_5=0, a_4<0, δ≤0,-(-8a_4)~(1/2)相似文献