On global solutions of functional differential equations

We construct a system of linear differential equations all solutions of which are global solutions of a system of functional differential equations. We substantiate the existence of this system and examine some properties of its solutions.     

Existence and comparison results for solutions of random integral and differential equations

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].     

Existence of solutions of systems of partial differential equations of fractional order

We obtain sufficient conditions for the existence and uniqueness of a solution of a system of partial differential equations of fractional order in spaces of integrable functions.Translated from Neliniini Kolyvannya, Vol. 7, No. 3, pp. 328–335, July–September, 2004.     

Analytical solutions of nonlinear system of fractional-order Van der Pol equations

Nonlinear Dynamics - The double-well, in-phase and out-of-phase periodic solutions of the system of fractional-order Van der Pol equations and the exact solution of the nonlinear fractional-order...     

Existence and comparison results of solutions for nonlinear random integral and differential equations relative to weak topology

In this paper, we prove several existence theorems of random solutions to nonlinear random Volterra integral equations under the weak topology of Banach spaces. Then, as applications, we obtain the existence theorems of weak random solutions to random differential equations. Existence of extremal random solutions and a random comparison theorem for these random equations are also obtained. Our theorems improve and extend the corresponding results in [4,5,10,11,12]. Projects supported by the Science Fund of the Chinese Academy of Sciences.     

Existence of solutions for implicit fuzzy differential inclusions

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.     

Existence and uniqueness of solutions for initial value problems of second order ordinary differential equations in Banach spaces

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]…     

Spatial local solutions of the Navier-Stokes equations

This paper considers solutions of the Navier-Stokes equations polynomial in the coordinates, which. are called local solutions. For an incompressible fluid, all higher-order terms (sums of higher-order. monomials) of degree 2 are found and it is proved that nontrivial axisymmetric higher-order terms. of degree higher than 2 do not exist. Nonsolenoidal axisymmetric solutions are listed, which can be. treated as steady-state barotropic gas flows in a potential external-force field. All elliptic vortices. generalizing the well-known Kirchhoff solution are calculated. All solutions of degree 3 with the. higher-order term of partial form are found. Some of these solutions break down in a finite time. regardless of the value and sign of viscosity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 109–119, March–April, 2009.     

Existence and attractivity results for nonlinear first-order random differential equations

istence and attractivity results are proved for nonlinear first-order ordinary random differential equations. An example is given to demonstrate a realization of the abstract theory developed in the present paper.     

EXISTENCE THEOREMS OF SOLUTIONS FOR TWO－POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

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Existence of solutions to differential inclusions in Banach spaces

I.IntroductionOwingtothefactthatthesystemwithwhicheconomics,biologyandsoonaredefinitelyconcernedtohaveuncertainty,includingthatcausedbyrestrictiononknowledge.asformathematicaltreatment,generallytheycanonlybedescribedbymeansofdifferentialinclusionsinsteadofdifferentialequations.Itiswell-knownthatthederivativex')ofasolutionx.)tothedifferentialequationx'(t)=f(t,x(t))inheritsthereqularityproperitiesofthemapfandthefunctionx(').Thisisnolongerthecasewithdifferentialinclusionsandisoneofthereasonswhyt…     

Numerical solutions of differential equations with fractional L-derivative

Fractional differential equations are solved with L-fractional derivatives, using numerical procedures. Two characteristic fractional differential equations are numerically solved. The first equation describes the motion of a thin rigid plate immersed in a Newtonian fluid connected by a massless spring to a fixed point, and the other one the diffusion of gas in a fluid.     

Systems of nonlinear differential equations with bounded solutions

We establish sufficient conditions for the existence of solutions bounded on ℝ for the equation {fx168-01}, in a finite-dimensional Banach space {ie168-01}. __________ Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 160–167, April–June, 2008.     

Existence of the vortex solutions of some semilinear elliptic equations

The purpose is to extend the existence result of vortex solutions to semilinear elliptic equations for a large class of nonlinearities. M. I. Weinstein used variational techniques to show the existence of nodal solutions for the specific nonlinear term f(¦¦)=(1–¦¦²). An ordinary differential equation phase space setting is used to show the unique transverse intersection of unstable and stable manifolds which contain the solutions satisfying the necessary boundary conditions under certain assumptions on the nonlinearity.