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C. Tunç 《Nonlinear Oscillations》2009,12(1):123-132
The main purpose of this paper is to give a result with explanatory example that deals directly with the instability of the
trivial solution of a certain nonlinear vector differential equation of the fourth order. The result established here improves
and includes a well-known instability result established for a scalar nonlinear differential equation of the fourth order.
Published in Neliniini Kolyvannya, Vol. 12, No. 1, pp. 120–129, January–March, 2009. 相似文献
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Interior layer behavior of boundary value problems for second order vector equation of elliptic type
In this paper, making use of the theory of partial differential inequalities, we will investigate the boundary value problems
for a class of singularly perturbed second order vector elliptic equations, and obtain the existence and asymptotic estimation
of solutions, involving the interior layer behavior, of the problems described above. 相似文献
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The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations 总被引:4,自引:0,他引:4
Robert Jensen 《Archive for Rational Mechanics and Analysis》1988,101(1):1-27
We prove that viscosity solutions in W
1, of the second order, fully nonlinear, equation F(D
2
u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) F is uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions, respectively. This method is completely different from that used in Lions [8, 9] for second order problems with F convex in D
2
u and from that used by Crandall & Lions [3] and Crandall, Evans & Lions [2] for fully nonlinear first order problems.The research reported here was supported in part by grants from the Alfred P. Sloan Foundation and the National Science Foundation. 相似文献
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金山 《应用数学和力学(英文版)》1987,8(6):547-559
In this paper, we study singular perturbation problems of some semi-linear second order elliptic equations with nonlinear boundary value conditions: where ε is a small positive parameter and u/ l is a directional derivative, which lies on an oblique vector (x,ε). We have given a construction of the asymptotic solutions and proof of their asymptotic correctness, which is based on the principle of contraction mapping. 相似文献
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A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in HI-norm. Furthermore, it is shown that the L^2 error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results. 相似文献
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1 IntroductionandMainRrsultsSincethe 1 950s,therehasbeenarapidprogressinthestudyoftheregularitytheoryforgeneralizedsolutionsofsecond_orderlinearellipticequationsindivergenceformwithseveralvariables,whichhasplayedanimportantroleinthestudyofquasi_linearequations (seeRefs.[1 ,2 ] ) .But,inspiteofthefactthatMorry[3 ]provedtheFredholmAlternativetheoremwithrespecttotheexistenceofgeneralizedsolutionsofsecond_orderlinearellipticequationsindivergenceform (whichisageneralizationoftheclassicaltheory)a… 相似文献
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We study isolated singularities of the quasilinear equation
in an open set of
N
, where 1 < p N, p -1 q < N(p — 1)/ (N -p). We prove that, for any positive solution, if a singularity at the origin is not removable then either
or u(x)/(x) any positive constant as x 0 where is the fundamental solution of the p-harmonic equation:
. Global positive solutions are also classified. 相似文献
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乔宗椿 《应用数学和力学(英文版)》1991,12(7):697-704
In this paper we study the asymptotic expansions of the solutions for a class of secondorder ordinary differential equations with slowly varying coefficients.The defect of theknown works on these problems is noted,and the results in[1—4]are improved andextended by means of the modified method of multiple scales. 相似文献
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Communicated by P. H. Rabinowitz 相似文献
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We propose sufficient conditions for the existence of a periodic solution of a system of linear ordinary differential equations
of the second order with a degenerate symmetric matrix in the coefficient of the second-order derivative in the case of an
arbitrary periodic inhomogeneity. 相似文献
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EXISTENCETHEOREMSOFSOLUTIONSFORTWO-POINTBOUNDARYVALUEPROBLEMOFSECONDORDERORDINARYDIFFERENTIALEQUATIONSINBANACHSPACESZhangShis... 相似文献
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IntroductionLet(E,l'I)denotearealBanachspacewithapartialorderintroducedbyanormalconeKofE.Inthispaper,weshallconsiderthefollowinginitialvalueproblemofsecondorderordinarydifferentialequation(IVP):wheref:JxEZ~EandJ=LO,TiforT>0.AfunctionxeCI(J,E)issaidtobeasolutionofIVP(I)ifithasabsolutelycontinuousfirstderivativeandsatisfies(I)fora.e.teJ.Theuseofmonotonemethodsinthestudyoftheinitial(boundary)valueproblemsofordinarydiffferentialequationshasrecentlybeenquiteextensive(see,forexample[I~8]… 相似文献