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1.
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
2.
A class of implicit fuzzy differential inclusions(IFDIs) are introduced and studied.Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation,respectively.A viable solution for a closed IFDI is proved to exist under the tangential condition.As an application,an implicit fuzzy differential equation,which comes from the drilling dynamics in petroleum engineering,is analyzed numerically.The obtained results can improve and extend some known results for fuzzy differential inclusions(FDIs) and fuzzy differential equations(FDEs),which might be helpful in the analysis of fuzzy dynamic systems. 相似文献
3.
The periodic problem of evolution inclusion is studied and its results are used toestablish existence theorems of periodic solutions of a class of semi-linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given forthis class of semi-linear differential inclusion. An application to some feedback control systems isdiscussed. 相似文献
4.
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
5.
In this paper, the new forms of the differential equations of motion of the systems with higher-order nonholonomic constraints are obtained at first, and then the equivalence between these equations and the known equations is demonstrated. Finally an example is given to illustrate the application of our new equations. 相似文献
6.
THE NUMERICAL SOLUTION OF A SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR PARABOLIC DIFFERENTIAL EQUATION 总被引:1,自引:0,他引:1
The numerical solution of a singularly perturbed problem for the semilinear parabolicdifferential equation with parabolic boundary layers is discussed.A nonlinear two-leveldifference scheme is constructed on the special non-uniform grids.The uniform convergenceof this scheme is proved and some numerical examples are given. 相似文献
7.
Gao Yongxin 《应用数学和力学(英文版)》1996,17(6):569-576
In this paper, the author uses the methods in [1, 2] to study the existence of solutions of three point boundary value problems for nonlinear fourth order differential equation.% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaCa% aaleqabaGaaiikaiaaisdacaGGPaaaaOGaeyypa0JaaGOKbiaacIca% caWG0bGaaiilaiaadMhacaGGSaGabmyEayaafaGaaiilaiqadMhaga% GbaiaacYcaceWG5bGbaibacaGGPaaaaa!4497!\[y^{(4)} = f(t,y,y',y',y')\] with the boundary conditions% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiGaaqaabe% qaaiaadEgacaGGOaGaamyEaiaacIcacaWGHbGaaiykaiaacYcaceWG% 5bGbauaacaGGOaGaamyyaiaacMcacaGGSaGabmyEayaagaGaaiikai% aadggacaGGPaGaaiilaiqadMhagaGeaiaacIcacaWGHbGaaiykaiaa% cMcacqGH9aqpcaaIWaGaaiilaiaadIgacaGGOaGaamyEaiaacIcaca% WGIbGaaiykaiaacYcaceWG5bGbayaacaGGOaGaamOyaiaacMcacaGG% PaGaeyypa0JaaGimaaqaaiqadMhagaqbaiaacIcacaWGIbGaaiykai% abg2da9iaadkgadaWgaaWcbaGaaGymaaqabaGccaGGSaGaam4Aaiaa% cIcacaWG5bGaaiikaiaadogacaGGPaGaaiilaiqadMhagaqbaiaacI% cacaWGJbGaaiykaiaacYcaceWG5bGbayaacaGGOaGaam4yaiaacMca% caGGSaGabmyEayaasaGaaiikaiaadogacaGGPaGaaiykaiabg2da9i% aaicdaaaGaayzFaaaaaa!7059!\[\left. \begin{gathered} g(y(a),y'(a),y'(a),y'(a)) = 0,h(y(b),y'(b)) = 0 \hfill \\ y'(b) = b_1 ,k(y(c),y'(c),y'(c),y'(c)) = 0 \hfill \\ \end{gathered} \right\}\] For the boundary value problems of nonlinear fourth order differential equation% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaCa% aaleqabaGaaiikaiaaisdacaGGPaaaaOGaeyypa0JaaGOKbiaacIca% caWG0bGaaiilaiaadMhacaGGSaGabmyEayaafaGaaiilaiqadMhaga% GbaiaacYcaceWG5bGbaibacaGGPaaaaa!4497!\[y^{(4)} = f(t,y,y',y',y')\] many results have been given at the present time. But the existence of solutions of boundary value problem (*). (**) studied in this paper has not been involved by the above researches. Morcover, the corollary of the important theorem in this paper, i. e. existence of solutions of the boundary value problem of equation (*) with the following boundary conditions.% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGHb% WaaSbaaSqaaiaaicdaaeqaaOGaamyEaiaacIcacaWGHbGaaiykaiab% gUcaRiaadggadaWgaaWcbaGaaGymaaqabaGcceWG5bGbauaacaGGOa% GaamyyaiaacMcacqGHRaWkcaWGHbWaaSbaaSqaaiaaikdaaeqaaOGa% bmyEayaagaGaaiikaiaadggacaGGPaGaey4kaSIaamyyamaaBaaale% aacaaIZaaabeaakiqadMhagaGeaiaacIcacaWGHbGaaiykaiabg2da% 9iaadMhadaWgaaWcbaGaaGimaaqabaGccaGGSaGaamOyamaaBaaale% aacaaIWaaabeaakiaadMhacaGGOaGaamOyaiaacMcacqGHRaWkcaWG% IbWaaSbaaSqaaiaaikdaaeqaaOGabmyEayaagaGaaiikaiaadkgaca% GGPaGaeyypa0JaamyEamaaBaaaleaacaaIXaaabeaaaOqaaiqadMha% gaqbaiaacIcacaWGIbGaaiykaiabg2da9iaadMhadaWgaaWcbaGaaG% OmaaqabaGccaGGSaGaam4yamaaBaaaleaacaaIWaaabeaakiaadMha% caGGOaGaam4yaiaacMcacqGHRaWkcaWGJbWaaSbaaSqaaiaaigdaae% qaaOGabmyEayaafaGaaiikaiaadogacaGGPaGaey4kaSIaam4yamaa% BaaaleaacaaIYaaabeaakiqadMhagaGbaiaacIcacaWGJbGaaiykai% abgUcaRiqadogagaGeaiaacIcacaWGJbGaaiykaiabg2da9iaadMha% daWgaaWcbaGaaG4maaqabaaaaaa!7DF7!\[\begin{gathered} a_0 y(a) + a_1 y'(a) + a_2 y'(a) + a_3 y'(a) = y_0 ,b_0 y(b) + b_2 y'(b) = y_1 \hfill \\ y'(b) = y_2 ,c_0 y(c) + c_1 y'(c) + c_2 y'(c) + c'(c) = y_3 \hfill \\ \end{gathered} \] has not been dealt with in previous works. 相似文献
8.
A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented.An iterative algorithm for approximating the solutions of generalized implicit variationallike inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved. 相似文献
9.
In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations (PDEs) with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu's method, in differential equations. 相似文献
10.
张石生 《应用数学和力学(英文版)》1999,20(6):585-592
The purpose of this paper is to introduce and study the existence of solutions and convergence of Mann and Ishikawa iterative
processes for a class of variational inclusions with accretive type mappings in Banach spaces. The results presented in this
paper extend and improve the corresponding results by Chang, Ding, Hassouni, Kazmi, Siddiqi, Zeng et al.
Foundation item: the National Natural Science Foundation of China (19771058) 相似文献
11.
GLOBAL SOLUTION OF THE INVERSE PROBLEM FOR ACLASS OF NONLINEAR EVOLUTION EQUATIONSOF DISPERSIVE TYPE
IntroductionItiswell_knownthatpseudo_parabolicequationwithprincipalpartut -uxxthasbeenstudyingrecently ,becausethereexistswidephysicalbackgroundforthisclassofequations.[1 ]studiedthemulti_dimensioninverseproblemforthefollowingclassofnonlinearevolutionequ… 相似文献
12.
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
13.
The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear
evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence
and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to
the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear
evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence
and uniqueness of local solution presented by YUAN Zhong-xin.
Contributed by Chen Yu-shu
Foundation item: the National Natural Science Foundation of China (Significance 199990510); the National Key Basic Research Special Foundation
of China (G1998020316); Liuhui Center for Applied Mathematics, Nankai University & Tianjin University
Biography: Chen Fang-qi (1963-) 相似文献
14.
丁协平 《应用数学和力学(英文版)》1986,7(7):643-650
This paper is the continuation of [1]. In this paper, we give another criteria of the existence of solutions for nonlinear random Volterra integral. A comparison theorem and the existence of random extremal solutions are also obtained by using the notion of ordering with respect to a cone. Our theorems generalize the corresponding results of Vaughan[2,3] and Lakshmikantham[4,5]. 相似文献
15.
The problem of the motion of a filtration front in a zero background in the case of a power-law dependence of the filtration coefficient on gas density is considered, and the existence and uniqueness theorem for solutions in the class of analytic functions is proved. The solution is constructed in explicit form, recurrence formulas for computing the coefficients in the series are obtained, and the convergence of the series is proved by the majorant method. The filtration front construction procedure is proposed. 相似文献
16.
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
17.
Instability of solution for the fourth order linear differential equation with varied coefficient 总被引:1,自引:0,他引:1
In this paper,we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient,at least one of the characteristic roots of which has positive real part,by means of Liapunov’s second method. 相似文献
18.
David E. Gilsinn 《Nonlinear dynamics》2007,50(1-2):73-92
In this paper, we prove a result that says: Given an approximate solution and frequency to a periodic solution of an autonomous
delay differential equation that satisfies a certain noncriticality condition, there is an exact periodic solution and frequency
in a neighborhood of the approximate solution and frequency and, furthermore, numerical estimates of the size of the neighborhood
are computed. Methods are outlined for estimating the parameters required to compute the errors. An application to a Van der
Pol oscillator with delay in the nonlinear terms is given. 相似文献
19.
丁协平 《应用数学和力学(英文版)》1985,6(3):269-275
In [1], we proved a general rondom fixed point theorem and gave some applications. In this paper, we shall give further applications of the theorem. We first obtain a rondom Darbo’s fixed point theorem, using the theorem, we give the criteria for the existence of solutions under compactness hypotheses to nonlinear rondom volterra integral equations and the Cauchy problem of nonlinear rondom differential equations. Our theorems improve andgeneralize some main results of Lakshmikanthem[2], Vaughn[3,4] as well as De Blasi and Myjak[5]. 相似文献
20.
IntroductionLetC(k- 1)2π =h(t) |h :R →Ris (k -1 )_thordercontinuousdifferentiableandh(t+ 2π) ≡h(t) , C2π =h(t) |h :R →Riscontinuousandh(t+ 2π) ≡h(t) , ‖h(t)‖ =supt∈ [0 ,2π] |h(t) | , ‖h(t)‖Pk- 1 =max‖h(t)‖ ,‖h′(t)‖ ,… ,‖h(k- 1) (t)‖ , x(m) (t+ ·) (θ) =x(m) (t+θ) θ∈R (m =0 ,1 ,2 ,… ,k-1 ) .Clearly ,x(m) (t + ·) ∈C2π, … 相似文献