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1.
王志华 《应用数学和力学(英文版)》1999,20(6):675-682
In this paper, the periodic viable trajectories of differential inclusions are discussed. Firstly, a simplified property of
differential inclusions is given. Then, an existence theorem of periodic viable trajectories of differential inclusions in
a finite dimensional space is proved. With the above results and Galerkin’s approximation, an existence theorem of periodic
viable trajectories of partial differential inclusions in a Hilbert space is proved. 相似文献
2.
宋福民 《应用数学和力学(英文版)》1998,19(11):1103-1113
I.IntroductionOwingtothefactthatthesystemwithwhicheconomics,biologyandsoonaredefinitelyconcernedtohaveuncertainty,includingthatcausedbyrestrictiononknowledge.asformathematicaltreatment,generallytheycanonlybedescribedbymeansofdifferentialinclusionsinsteadofdifferentialequations.Itiswell-knownthatthederivativex')ofasolutionx.)tothedifferentialequationx'(t)=f(t,x(t))inheritsthereqularityproperitiesofthemapfandthefunctionx(').Thisisnolongerthecasewithdifferentialinclusionsandisoneofthereasonswhyt… 相似文献
3.
Proximal point algorithm with errors for generalized strongly nonlinear quasivariational inclusions 总被引:1,自引:0,他引:1
丁协平 《应用数学和力学(英文版)》1998,19(7):637-643
I.IntroductionLetHbeaHibertspaceendowedwithanorm11'11andaninnerproduct',.)andC(H)bethefamilyofallnonemptycompactsubsetsofH.LetT,A:H~C(H)besetvaluedmappings,g:H~Hbeasingle-valuedmappingand9:HxH~RU{ ac}besuchthatforeachfixedyeH,9.,y):H~RUt co}isaproperconvexlowersemicontinuousfunctiononHandg(H)ndomag'Y)#oforeachyeH,ThentheproblemoffindingxeH,ueT(x)andveA(x)suchthatg(x)edomag',x)and(u~v,y~g(x))39(g(x)'x)~9(y'x)(VYeH)(l.l)iscalledthegeneralizedstronglynonlinearquasivariationalinclusio… 相似文献
4.
THEEXISTENCEOFPERIODICSOLUTIONSFORACLASSOFFUNCTIONALDIFFERENTIALEQUATIONSANDTHEIRAPPLICATIONZhaoJie-min(赵杰民);HuangKe-lei(黄克累)... 相似文献
5.
Blow-Up Estimates for a Non-Newtonian Filtration System 总被引:2,自引:0,他引:2
IntroductionandProblemintheResearchofToroidThestructureofpositivesolutionsforquasi_linearreaction_diffusionsystems (nonlinearNewtonianfiltrationsystems)andsemi_linearreaction_diffusionsystems (Newtonianfiltrationsystems)isahottopicinthestudyofnonlineard… 相似文献
6.
Periodic Traveling Waves for Diffusion Equations with Time Delayed and Non-local Responding Reaction 总被引:6,自引:0,他引:6
We develop a singular perturbation technique to study the existence of periodic traveling wave solutions with large wave speed
for a class of reaction-diffusion equations with time delay and non-local response. Unlike the classical singular perturbation
method, our approach is based on a transformation of the differential equations to integral equations in a Banach space that
reduces the singular perturbation problem to a regular perturbation problem. The periodic traveling wave solutions then are
obtained by the use of Liapunov-Schmidt method and a generalized implicit function theorem. The general result obtained has
been applied to a non-local reaction-diffusion equation derived from an age-structured population model with a logistic type
of birth function. 相似文献
7.
房辉 《应用数学和力学(英文版)》2000,21(3):291-296
1 ProblemintheResearchofToroidImpulsivedifferentialequationisanewimportantbranchofdifferentialequation.In1989,[1],[2]systematicallysummarizedresearchworkaboutimpulsiveordinarydifferentialequations.Inrecentyears,therearemanyliteraturesdealingwiththeoscillatio… 相似文献
8.
Toka Diagana 《Nonlinear dynamics》2006,45(1-2):45-53
This paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to a class of semilinear differential
equations involving the algebraic sum of two (possibly noncommuting) densely defined closed linear operators acting on a Hilbert
space. Sufficient conditions for the existence and uniqueness of pseudo almost periodic solutions to those semilinear equations
are obtained.
An erratum to this article is available at . 相似文献
9.
Systems of generalized quasi-variational inclusion (disclusion) problems in FC-spaces 总被引:1,自引:0,他引:1
丁协平 《应用数学和力学(英文版)》2010,31(5):545-556
By applying an existence theorem of maximal elements of set-valued mappings in FC-spaces proposed by the author, some new existence theorems of solutions for systems of generalized quasi-variational inclusion (disclusion) problems are proved in FC-spaces without convexity structures. These results improve and generalize some results in recent publications from closed convex subsets of topological vector spaces to FC-spaces under weaker conditions. 相似文献
10.
Optimal Existence Theory for Single and Multiple Positive Periodic Solutions of Functional Differential Equations 总被引:1,自引:0,他引:1
This paper deals with a new optimal existence theory for single and multiple positive periodic solutions of functional differential equations using a fixed-point theorem in cones. We illustrate our theory by examining several biomathematical models. The paper improves and extends previous results in the literature. 相似文献
11.
A class of nonlinear elliptic problems driven by p(x)-Laplacian with a nonsmooth locally Lipschitz potential is considered.By applying the version of the nonsmooth three-critical-point theorem,the existence of three solutions to the problems is proved. 相似文献
12.
丁协平 《应用数学和力学(英文版)》1999,20(10):1087-1098
IntroductionVariationalinequalitytheoryandcomplementarityproblemtheoryhavebecomeveryeffectiveandpowerfultoolsforstudyingawiderangeofproblemsarisinginmechanics,mathematicalprogramming,optimizationandcontrol,equilibriumtheoryofeconomics,managementscien… 相似文献
13.
In this paper, a new model with two state impulses is proposed for pest management. According to different thresholds, an integrated strategy of pest management is considered, that is to say if the density of the pest population reaches the lower threshold \(h_1\) at which pests cause slight damage to the forest, biological control (releasing natural enemy) will be taken to control pests; while if the density of the pest population reaches the higher threshold \(h_2\) at which pests cause serious damage to the forest, both chemical control (spraying pesticide) and biological control (releasing natural enemy) will be taken at the same time. For the model, firstly, we qualitatively analyse its singularity. Then, we investigate the existence of periodic solution by successor functions and Poincaré-Bendixson theorem and the stability of periodic solution by the stability theorem for periodic solutions of impulsive differential equations. Lastly, we use numerical simulations to illustrate our theoretical results. 相似文献
14.
张永新 《应用数学和力学(英文版)》2009,30(10):1335-1344
In this paper, we aim to find eventually vanished solutions, a special class of bounded solutions which tend to 0 as t → ±∞), to a Lienard system with a time-dependent force. Since it is not a Hamiltonian system with small perturbations, the well-known Melnikov method is not applicable to the determination of the existence of eventually vanished solutions. We use a sequence of periodically forced systems to approximate the considered system, and find their periodic solutions. Difficulties caused by the non- Hamiltonian form are overcome by applying the Schauder's fixed point theorem. We show that the sequence of the periodic solutions has an accumulation giving an eventually vanished solution of the forced Lienard system. 相似文献
15.
Based upon the conservation of average energy a theorem about the periodic solutions of strongly nonlinear nonautomous systems with multi-degree-of freedom is proved. This theorem can not only decide the existence and stability of the periodic solutions, but at the same time can also give their first-order and second-order approximate expressions. 相似文献
16.
云天铨 《应用数学和力学(英文版)》2001,22(10):1132-1139
IntroductionManystudieshavebeendoneoncontractivemappings,e .g .,Rhoades[1]madeacomparisonofvariousdefinitions (morethan 1 0 0typesvariedfrom 2 5basictypes)ofcontractivemappingoncompletemetricspacein 1 977.Anduptonow ,suchstudyisstillgoingon ,e .g .,[2 ] .Inthispaper,these… 相似文献
17.
In this paper, based upon the concept of the conservation of average energy, a theorem for the periodic solution of strongly nonlinear nonautonomous systems is proved. By using this theorem not only the necessary and sufficient conditions for the existence and stability of the periodic solutions can be obtained but, at the same time, the approximate expressions for those periodic solutions can also be obtained. 相似文献
18.
In this paper, we prove the existence of small amplitude, smooth time quasi-periodic solutions for a class of reversible derivative nonlinear Schrödinger equations with periodic boundary conditions. The proof is based on an abstract Kolmogorov–Arnold–Moser(KAM) theorem for infinite dimensional reversible system. 相似文献
19.
This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system. 相似文献
20.
张石生 《应用数学和力学(英文版)》2004,25(6)
The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces.By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established.The results generalize,improve and unify a number of Noor's and others' recent results. 相似文献