exponential and logarithm equations

... 2.25 are yo (0) = and yo (0) = Setting t = in the above ˙ equations and using the initial conditions, we obtain K + K2 = − K1 − 2K2 = and Solution of these equations yields K1 = and K2 = −1 Therefore, ... Setting k = and in Eq 2.59 and substituting h[0] = 0, h[1] = yields = + A1 + A2 = A1 + 2A2 and Solution of these two equations yields A1 = −3 and A2 = Therefore, h[k] = δ[k] − + 2(2)k and from Eq ... Ordinary Linear Differential and Difference Equations 2.1 Differential Equations Classical Solution • Method of Convolution 2.2 Difference Equations Initial Conditions and Iterative Solution • Classical...

Ngày tải lên: 27/01/2014, 03:20

... u≥0 in Ω, were studied in detail by B´nilan and Brezis, Baras and Pierre, and Marcus and e V´ron analytically for < q < ∞, and by Le Gall, and Dynkin and Kuznetsov e using probabilistic methods ... Adams and Pierre [AP], Baras and Pierre [BP], Berestycki, CapuzzoDolcetta, and Nirenberg [BCDN], Brezis and Cabr´ [BC], Kalton and Verbitsky e [KV] It is worth mentioning that related equations ... operators, and distributed singularities, and develop the theory simultaneously for quasilinear equations and equations of Monge-Amp`re type e Introduction We study a class of quasilinear and fully...

Ngày tải lên: 15/03/2014, 09:20

... J A Trujillo Ferreras, R Williams, M Yor, and Yong Zeng Th Jeulin, K Shimbo, and Yan Zeng gave extraordinary help, and my editor C Byrne gives advice and has patience that is impressive Over the ... Differential Equations: Continuity and Differentiability 301 Flows as Diffeomorphisms: The Continuous Case 310 General Stochastic Exponentials and ... semimartingales in the expanded filtration We next present the more difficult theory of progressive expansion, which involves expanding filtrations to turn a random time into a stopping time, and then analyzing...

Ngày tải lên: 08/04/2014, 12:25

Ngày tải lên: 13/05/2014, 12:16

... Ladyzhenskaya and N N Ural'tseva, Linear and quasilinear equations of elliptic type, and with the monograph of A Ladyzhenskaya, V A Solonnikov, and N N Ural'tseva, Linear and quasilinear equations ... for degenerate and nonuniformly elliptic and parabolic equations of second order and to the investigation of differential and certain qualitative properties of the solutions of such equations The ... degenerate and nonuniformly elliptic and parabolic equations of second order, and also to the investigation of differential and certain qualitative properties of solutions of such equations A...

Ngày tải lên: 31/05/2014, 01:37

... theory of ordinary and delay differential equations lead to investigations of functional differential equations of various types see the books by Hale and Verduyn Lunel, Wu, and articles by Liang, ... kata, Benchohra, Lizama, Hernandez, etc and the references e e therein On the other hand, the theory of fractional differential equations is also intensively studied and finds numerous applications ... theory developed by J Nunziato, M E Gurtin, and A C Pipkin, the internal energy and the heat flux are described as functionals of u and ux An abstract and more general version of neutral system...

Ngày tải lên: 21/06/2014, 05:20

... T and space inversion P 43 This analysis of the fractional wave, diffusion, and Dirac equations, fits in the general context of establish bridges between fractional calculus and the classical and ... AYA2009-14212-C05-05 and by FCT and POCI 2010 Project MAT/58321/2004 with participation of FEDER References S G Samko, A A Kilbas, and O I Marichev, Fractional Integrals and Derivatives: Theory and Applications, ... Classical a and Quantum Aspects, F Kh Abdullaev and V V Konotop, Eds., pp 129–133, Kluwer Academic Publishers, New York, NY, USA, 2004 12 L V´ zquez and D Usero, “Nonlocal equations and fractional...

Ngày tải lên: 21/06/2014, 05:20

... · is the pairing between E and E∗ , d is the metric induced by the norm · , 2E resp., CB E is the family of nonempty resp., nonempty closed and bounded subsets of E, and H ·, · is the Housdorff ... ·,u z A Jη,M ·,u where ρ is a constant and Rη,M ·,u and I is the identity mapping Equation 2.17 is called the resolvent equation problem z Fixed Point Theory and Applications In support of problem ... xn−1 , yn−1 ρ m an − m an−1 By using the Lipschitz continuty of A, g, and m with constants λA , λg , and λm , respectively, and by Algorithm 3.3, we have A g un − m an − A g un−1 − m an−1 ≤ λA...

Ngày tải lên: 21/06/2014, 07:20

... Mathematics and Its Applications, Hindawi, Cairo, Egypt, 2007 N V Azbelev and P M Simonov, Stability of Differential Equations with Aftereffect, vol 20 of Stability and Control: Theory, Methods and Applications, ... Difference Equations, vol 2009, Article ID 671625, 15 pages, 2009 N V Azbelev, V P Maksimov, and L F Rakhmatullina, Introduction to the Theory of Functional Differential Equations: Methods and Applications, ... inequality and a linear delay equation Similar in a sense problems for delay difference equations were studied in 5, as well This paper aims to investigate the problems of the existence, uniqueness and...

Ngày tải lên: 21/06/2014, 20:20

... last variable and which, for every λ ∈ [0,1], satisfies that χ(·, ·,λ) is a random operator A measurable map (a random variable) x : Ω → X ∩ Y is said to be a random fixed-point of a random operator ... 154 Nielsen number and differential equations one can prove (see [5] or [9]) that Tτ is a random operator with compact values, composed of a random operator with Rδ -values and the continuous ... continuous self-map of Tn and τ is a positive number (3.33) Jan Andres 155 Remark 3.6 Examples 3.2 and 3.4 can then be appropriately randomized as well 3.6 ad (f) Let M ∈ R and let ΓM := {(t,x) ∈...

Ngày tải lên: 23/06/2014, 00:20

... systems of functional equations with two variables Let P(x; v) = (pij (x; v))1≤i,j≤ and Q(x; v) = (qij (x; v))1≤i,j≤ be any two × matrices of rational functions in x and v, and b(x; v) = (b1 (x; ... Numbers, and Some Unsolved Problems In Combinatorics, Geometry, and Probability: A Tribute to Paul Erd˝s, Trinity College, Cambridge, o March 1993 (Ed B Bollob´s and A Thomason) Cambridge, England: ... functional equations As mentioned before, our method yields a multivariate system of functional equations in several variables, which is hard to solve in general (several cases of functional equations...

Ngày tải lên: 07/08/2014, 13:21

... equations for Fagus trees 445   Figure Generalised equations for (a) stem (b) branches and (c) foliage biomass together with the pooled datasets from the Spanish and Greek stand The Spanish and ... (9) and original equations for aboveground biomass MT) Figure Predicted values for aboveground biomass (MT) from the generalised equation (10) and from original equations for the (a) Spanish and ... published equations, for total and stem biomass (Tab V) The mean percentage difference between values obtained by generalised equations and those predicted by individual regressions for branch and...

Ngày tải lên: 08/08/2014, 01:21

... Meerschaert / Statistics and Probability Letters 79 (2009) 1596–1601 1599 Proof The result follows from (1.2) and well-known moment conditions and formulas for standard exponential and standard α -stable ... distributed random variable (1.7), the variables {Y (pi) } are IID for each p, and Np and {Y (pi) } are independent (see, e.g., Klebanov et al., 1984) It is well known that both exponential and ML ... and domains of attraction Operator stable random vectors are the weak distributional limits of sums of independent and identically distributed random vectors Given U , U (1) , U (2) IID random...

Ngày tải lên: 05/07/2015, 10:00

... been appreciably extended, and includes not only ordinary differential equations and classical dynamical systems, but wide classes of partial differential equations and equations in Banach spaces ... and the compactness of solutions Almost periodic solutions of the evolution equation Comments and references to the literature Linear equations in a Banach space (questions of admissibility and ... Almost periodic functions and differential equations Almost periodic functions and differential equations B.M.LEVITAN & V.V.ZHIKOV Translated by L W Longdon...

Ngày tải lên: 29/10/2015, 12:29

... and (ii) are treated in Sections and 6, respectively Sections and are devoted to step (iii) Sections and 10 are concerned with Steps (iv) and (v) Section 11 deals with steps (vi) and (vii), and ... real case: α1 , α2 and α3 are real numbers > 1, and the logarithms of the αi ’s are real (and > 0), • the complex case: α1 , α2 and α3 are complex numbers of modulus one, and the logarithms of the ... Proposition 10.1 and we omit almost all the details We can take K(l) = l − in this case, and we let En and E be given by equations (24) and (25) respectively If l ≡ ±1 (mod 5) and q ≥ are primes...

Ngày tải lên: 06/03/2014, 08:21

... > 0, and proved a global existence result for g ≥ and an exponential decay for g > This result has been extended by Messaoudi and Tatar [2,7] to the situation where g = and exponential and polynomial ... restrictions and −ξ1 g(t) ≤ g (t) ≤ −ξ2 g(t), t ≥ 0, the authors established an exponential rate of decay This latter result has been improved by Cavalcanti and Oquendo [5] and Berrimi and Messaoudi ... conditions on the initial data to handle the source terms Unfortunately, due to the strong nonlinearities on f1 and f2, the techniques used by Han and Wang [19] and Agre and Rammaha [22] allowed them...

Ngày tải lên: 21/06/2014, 00:20

... Minh, F R¨ biger, and R Schnaubelt, Exponential stability, exponential expansiveness, and a exponential dichotomy of evolution equations on the half-line,” Integral Equations and Operator Theory, ... Analysis and Applications, vol 129, no 2, pp 362–374, 1988 S Elaydi and O H´ jek, Exponential dichotomy and trichotomy of nonlinear differential equations, ” a Differential and Integral Equations, ... 1991 A L Sasu and B Sasu, Exponential trichotomy for variational difference equations, ” Journal of Difference Equations and Applications, vol 15, no 7, pp 693–718, 2009 B.-G Wang and W.-T Li, “Limit...

Ngày tải lên: 21/06/2014, 05:20

... Difference Equations and uniqueness of the solutions to random impulsive differential equations, and in 18 Zhao and Zhang discussed the exponential stability of random impulsive integro-differential equations ... to deal with the exponential stability of random impulsive integrodifferential equations in 18 and study the exponential stability in mean square of random impulsive differential equations in 19 ... the methods to discuss the exponential stability of deterministic impulsive differential equations of neutral type and the exponential stability for random differential equations can not be directly...

Ngày tải lên: 21/06/2014, 11:20

... to (1.1) is exponentially or uniformly exponentially stable on [0, ∞) Some of our results are new even for the special cases T = R and T = Z To understand the notation used above and the idea ... −1/2 and δ > −(2a + 1), then the trivial solution to (4.1) is uniformly exponentially stable 142 Exponential stability of dynamic equations on time scales Case 4.3 If T = N0 , then µ(t) = and ... p, δ > 0, L ≥ are constants and < ε < min{λ3 ,δ } Then the trivial solution of (1.1) is uniformly exponentially stable on [0, ∞) 140 Exponential stability of dynamic equations on time scales Proof...

Ngày tải lên: 23/06/2014, 00:20

... (1.7) where k and r are positive integers and the coefficients Ki and b are constants For other examples of higher-order difference equations with a positively homogeneous right-hand side, see, ... [7] [8] [9] [10] C T H Baker and A Tang, Generalized Halanay inequalities for Volterra functional differential equations and discretized versions, Volterra Equations and Applications (Arlington, ... following corollary of Theorems 2.5 and 3.1 E Liz and M Pituk 49 Corollary 3.2 Suppose that there exists µ ≥ such that f is continuous on Cµ and conditions (1.6), (2.3), and (2.16) hold Then, (1.8)...

Ngày tải lên: 23/06/2014, 00:20