APPLICATIONS OF SECOND ORDER DIFFERENTIAL EQUATIONS PPT

For higher-order functional differential equations and, particularly, for nonautonomous differentialequations with deviated arguments, new sufficient conditions for the existence and uniqueness of aperiodic solution are established.Copyright q 2008 I. Kiguradze et al. This is an ope[r]

attention has been paid to the existence, uniqueness, and spectrum containment of almostperiodic solutions of this type of equations see, e.g., 4–12 and reference there in.If g1t and g2t are almost periodic, then the module containment propertymodg1 ⊂ modg2 ca[r]

16.4.1. Fredholm Integral Equations of the Second Kind. Resolvent . . . . . . . . . . . . . . 82916.4.2. Fredholm Equations of the Second Kind with Degenerate Kernel . . . . . . . . . . 83016.4.3. Solution as a Power Series in the Parameter. Method of[r]

Hindawi Publishing CorporationBoundary Value ProblemsVolume 2010, Article ID 521070, 2 pagesdoi:10.1155/2010/521070EditorialDegenerate and Singular Differential Operatorswith Applications to Boundary Value ProblemsClaudianor Oliveira Alves1and Vicent¸iu R˘adulescu2, 31Unidade Acadˆemic[r]

Remark 1.1. All functional inequalities considered in this paper are assumed to holdeventually; that is, they are satisfied for all t large enough.Rem ark 1.2. Without loss of generality, we can deal only with the positive solutionsof (1.1).2. Main resultsIn this section, we will establish so[r]

¨auser, Boston, Mass, USA, 2001.3 M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales,Birkh¨auser, Boston, Mass,USA, 2003.4 S. Hilger, “Analysis on measure chains—a unified approach to continuous and discrete calculus,”Results in Mathematics, vol. 18, no. 1-2, pp. 18–56[r]

EXISTENCE RESULTS FOR φ-LAPLACIAN BOUNDARY VALUEPROBLEMS ON TIME SCALESALBERTO CABADAReceived 24 January 2006; Revised 31 May 2006; Accepted 1 June 2006This paper is devoted to proving the existence of the extremal solutions of a φ-Laplaciandynamic equation coupled with nonlinear bound[r]

+ Axn−k,JournalofDifference Equationsand Applications 11 (2005), no. 8, 701–705.[11] E. Liz and J. B. Ferreiro, A note on the global stability of generalized difference equations,AppliedMathematics Letters 15 (2002), no. 6, 655–659.[12] E. Liz and M. Pituk, Asymptotic estimates an[r]

AcknowledgmentsThe authors are very grateful to the referees for careful reading of the original manu-script and for valuable suggestions on improving this paper. This project is supported bythe Natural Science Foundation of Jiangsu Education Office (06KJB110010) and JiangsuPlanned Proj[r]

the NSF of China (no. 10671046).References[1] M.Biroli,“Surlessolutionsborn´ees ou presque p´eriodiques des´equations d’´evolution multivo-quessurunespacedeHilbert,”Ricerche di Matematica, vol. 21, pp. 17–47, 1972.[2] C. M. Dafermos, “Almost periodic processes and almost periodic solut[r]

ix =0, i = 1,2, is said to be oscillatory if all its solutions areoscillatory. It should be noted that the essentials of Sturmian theory have been extendedto the half-linear equation L2x =0(cf.ˇReh´ak [23]).One of the impor tant techniques used in studying oscillations of dynami[r]

, is zero, while the other ciis thesame, and in this case the right-hand side of equation (14.1.2.5) must contain the first-order partial derivativewith respect to yk.Remark 2. In turn, the hyperbolic equations are divided into normal hyperbolic equations—for whichall cibu[r]

1) < 1.We can also extend the discu ssion to the existence of at least one solut ion for inte-gro-differential equations of mixed type with “anti-periodic” conditions.x= f (t, x,(Kx)(t), (Lx )(t)), t ∈ [0, 1];x(0) = −x(1).We omit it here because it is trivial.Ack[r]

0,ξ v1ξ,ξ∈ Ω,3.1where Ω is a bounded open domain inN,withsufficiently smooth boundary ∂Ω and α, β, kas in Assumption 2.LetH  L2Ω with the usual inner product and norm. Here, we denoteby ∂tu the time derivative of u and by Δu the Laplacian of u with respect to space variable ξ.[r]

VỀ TÍNH DUY NHẤT NGHIỆM NHỚT CỦA PHƯƠNG TRÌNH ĐẠO HÀM RIÊNG CẤP HAI LOẠI PARABOLIC ON THE UNIQUENESS OF VISCOSITY SOLUTIONS TO SECOND ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS NGUYỄN CHÁNH ĐỊNH Trường Đại học Sư phạm, Đại học Đà Nẵng TÓM TẮT Lý thuyết nghi[r]

RESEARCH Open AccessComplementary tensor-driven image coherencediffusion for oriented structure enhancementZhang Hong-mei, Wan Ming-xi*and Bian Zheng-zhongAbstractOriented structure enhancement plays important role in computer vision tasks, where the diffusion is encouragedalong the preferred direct[r]

(s) = s|s|p−2.Letψqbe the inverse of ψp.2 Boundary Value ProblemsIn passing, we note that the monotone iterative technique developed in this paper isan application of Amann’s method [19] and the first term of the iterative scheme may betaken to be a constant function or a simple[r]

Hindawi Publishing CorporationBoundary Value ProblemsVolume 2011, Article ID 929061, 17 pagesdoi:10.1155/2011/929061Research ArticleApproximation of Solutions for Second-Orderm-Point Nonlocal Boundary Value Problems viathe Method of Generalized QuasilinearizationAhmed AlsaediDep[r]

´eTranscendents 49412.3.5. Perturbation Methods of Mechanics and Physics . . . . . . . . . . . . . . . . . . . . . . . 49912.3.6. Galerkin Method and Its Modifications (Projection Methods) . . . . . . . . . . . . . 50812.3.7. Iteration and Numerical Methods . . . . . . . . . . . . . . . . . .[r]