euler poincar´e equations on semidirect products

Ngày tải lên: 14/03/2014, 13:20

Ngày tải lên: 14/03/2014, 13:20

... Assouad dimension lowered through quasisymmetric mappings if and only if they possess at least one weak-tangent 578 STEPHEN KEITH AND XIAO ZHONG that contains a collection of non-constant rectifiable ... discussed further in Section 1.3 Outline In Section we recall terminology and known results The proof of Theorem 1.0.1 is contained in Section Section contains further discussion required for Remark ... AN OPEN ENDED CONDITION 585 The next proposition gives the local estimate of the level set of the fractional maximal function of u, and is the main result of this section Proposition 3.1.1 Let...

Ngày tải lên: 29/03/2014, 07:20

... beyond canonical formulations 1.4 Geometry, Symmetry and Reduction We have emphasized the distinction between canonical and non-canonical coordinates by contrasting Hamilton’s (canonical) equations ... functions F ” is equivalent to Hamilton’s equations In fact, it tells how any function F evolves along the flow This representation of the canonical equations of motion suggests a generalization ... bracket notation to cover non-canonical formulations As an example, consider Euler s equations Define the following non-canonical rigid body bracket of two smooth functions F and K on the angular...

Ngày tải lên: 24/04/2014, 16:49

... utilisation of the colorants in cosmetic products under current uses and practices? * Does the SCCNFP recommend additional restrictions on the use of these colorants in cosmetic products? Opinion on ... 4524-4527 IARC (1975) Monographs on the evaluation of the carcinogenic risk of chemicals to man Vol 8: Some aromatic azo compounds Lyon, France IARC (1982) Monographs on the evaluation of the carcinogenic ... restrictions on certain azo-colorants : Azo-dyes that may release, by reductive cleavage of one or more azo groups, one or more of the aromatic amines listed in Appendix, in concentrations above...

Ngày tải lên: 25/05/2014, 17:46

... Then, the condition f ∈ R (g, I) is equivalent to each one of the following items: (i) f is a monotonic function on I; (ii) f is a continuous function on I; (iii) f is regulated on I; (iv) f ... Δ-integral conditions for second-order dynamic equations on time scales at resonance Advances in Difference Equations 2011 2011:42 Submit your manuscript to a journal and benefit from: Convenient online ... Applications Birkhäuser, Boston (2001) Bohner, M, Peterson, A: Advances in Dynamic Equations on Time Scales Birkhäuser, Boston (2003) Agarwal, RP, O’Regan, D: Nonlinear boundary value problems on time...

Ngày tải lên: 20/06/2014, 22:20

... Peterson, Advances in Dynamic Equations on Time Scales, Birkh¨ user, Boston, Mass, a USA, 2003 M Bohner and S H Saker, “Oscillation of second order nonlinear dynamic equations on time scales,” The Rocky ... research activity concerning the oscillation and nonoscillation of solutions of various equations on time scales, and we refer the reader to 5–18 Recently, Erbe et al 19–21 considered the asymptotic ... Erbe, “Oscillation results for second-order linear equations on a time scale,” Journal of Difference Equations and Applications, vol 8, no 11, pp 1061–1071, 2002 T S Hassan, “Oscillation criteria...

Ngày tải lên: 21/06/2014, 05:20

... difference equations, ” International Journal of Difference Equations, vol 1, no 2, pp 181–193, 2006 P E Kloeden and A Zmorzynska, “Lyapunov functions for linear nonautonomous dynamical equations on time ... initial condition is equivalent to the condition Aρ t0 x t0 not also dependent on choice of projectors Noting that if x t is a solution of 2.3 with the initial condition 2.33 , then x t ∈ t0 Conversely, ... initial condition τ Aρ t0 x t0 − x0 3.2 has a unique solution defined on Ìt0 The condition ensuring the existence of a unique solution can be refered to Section We denote the solution with the...

Ngày tải lên: 21/06/2014, 05:20

... use the cone theory and monotone iterative technique to investigate the existence of minimal nonnegative solution for a class of second-order nonlinear impulsive differential equations on an infinite ... problems for second order impulsive integro-differential equations in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol 28, no 6, pp 983–997, 1997 X Liu, “Monotone iterative ... differential equations, ” Applied Mathematics and Computation, vol 202, no 2, pp 550–561, 2008 19 T Jankowski, “Existence of solutions for second order impulsive differential equations with deviating...

Ngày tải lên: 21/06/2014, 11:20

... semi-position condition In this article, we are concerned with the existence of positive solutions for the following PBVPs of impulsive dynamic equations on time scales with semi-position condition  ... Bohner, M, Peterson, A: Dynamic Equations on Time Scales: An Introduction with Applications Birkhauser, Boston (2001) [20] Bohner, M, Peterson, A: Advances in Dynamic Equations on Time Scales Birkhauser, ... for impulsive differential equations and impulsive difference equations have received much attention [4–18] On the other hand, recently, the theory of dynamic equations on time scales has become...

Ngày tải lên: 21/06/2014, 17:20

... Dynamic Equations on Time Scales, Birkh¨ user, Boston, Mass, a USA, 2003 11 M Bohner and A Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkh¨ user, Boston, Mass, ... solution for second order nonlinear differential equations, ” Applied Mathematics and Computation, vol 162, no 3, pp 1227–1235, 2005 W G Kelley and A C Peterson, Difference Equations: An Introduction ... 1.4 , one can easily obtain the Sturm comparison theorem of second-order linear differential equations 1.3 Sturm-Picone Comparison Theorem Assume that x t and y t are the nontrivial solutions of...

Ngày tải lên: 21/06/2014, 20:20

... Benchohra, S Hamani, and J Henderson, “Functional differential inclusions with integral boundary conditions,” Electronic Journal of Qualitative Theory of Differential Equations, vol 2007, no 15, pp 1–13, ... nonlinear ordinary differential equations of second order ¨ in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol 4, no 5, pp 985–999, 1980 32 S Szufla, On the application ... 18 N Heymans and I Podlubny, “Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives,” Rheologica Acta, vol 45, no 5,...

Ngày tải lên: 21/06/2014, 20:20

... Peterson, Dynamic Equations on Time Scales: An Introduction with Application, Birkh¨ user, Boston, Mass, USA, 2001 a R P Agarwal, M Bohner, and P Reh´ k, “Half-linear dynamic equations, ” in Nonlinear ... “Integration on measure chains,” in Proceedings of the 6th International Conference on Difference Equations, pp 239–252, CRC Press, Boca Raton, Fla, USA, 2004 11 K L Boey and P J Y Wong, “Positive ... pages, 2007 D R Anderson, “Solutions to second-order three-point problems on time scales,” Journal of Difference Equations and Applications, vol 8, no 8, pp 673–688, 2002 D R Anderson and I Y Karaca,...

Ngày tải lên: 21/06/2014, 20:20

... Bohner and A Peterson, Advances in Dynamic Equations on Time Scales, Birkh¨ user, Boston, Mass, a USA, 2003 L Erbe, “Oscillation results for second-order linear equations on a time scale,” Journal ... equations on time scales,” Computers & Mathematics with Applications, vol 49, no 4, pp 599–609, 2005 10 Y Sahiner, “Oscillation of second-order delay differential equations on time scales,” Nonlinear ... Difference Equations and Applications, vol 8, no 11, pp 1061–1071, 2002 S H Saker, “Oscillation criteria of second-order half-linear dynamic equations on time scales,” Journal of Computational and...

Ngày tải lên: 21/06/2014, 20:20

... Applications, vol 56, no 6, pp 1496–1504, 2008 10 Advances in Difference Equations 20 M Bohner and A Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkh¨ user, Boston, ... equations on time scales,” Nonlinear Analysis: Theory, Methods & Applications, vol 69, no 11, pp 4074– 4087, 2008 J R Graef and A Ouahab, “Extremal solutions for nonresonance impulsive functional ... integrodifferential equations in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol 68, no 9, pp 2727–2740, 2008 D Guo, “A class of second-order impulsive integro-differential equations on...

Ngày tải lên: 21/06/2014, 20:20

... for impulsive differential equations and impulsive difference equations have received much attention 9–19 On the other hand, recently, the theory of dynamic equations on time scales has become ... focused their attention on the boundary value problems of impulsive dynamic equations on time scales 20–27 In particular, for the first-order impulsive dynamic equations on time scales yΔ t p ... calculus on time scales and some of its applications,” Results in Mathematics, vol 35, no 1-2, pp 3–22, 1999 M Bohner and A Peterson, Dynamic Equations on Time Scales: An Introduction with Applications,...

Ngày tải lên: 21/06/2014, 20:20

... Dynamic Equations on Time Scales: An Introdution with Applications, Birkh¨ user, Boston, Mass, USA, 2001 a 23 M Bohner and A Peterson, Dynamic Equations on Time Scales, Birkh¨ user, Boston, Mass, ... nonautonomous impulsive differential equations, ” International Journal of Qualitative Theory of Differential Equations and Applications, vol 2, no 1, pp 112–124, 2008 22 M Bohner and A Peterson, ... “Variational approach to impulsive differential equations, ” Nonlinear Analysis: Real World Applications, vol 10, no 2, pp 680–690, 2009 21 H Zhang and Z X Li, “Periodic solutions of second-order nonautonomous...

Ngày tải lên: 21/06/2014, 20:20

... this class of nonautonomous scalar dynamic equations on time scales, the approach that authors used in this paper is based on Mawhin’s continuation theorem In this paper, we consider the existence ... fixed point theorem, two classes of one-order linear dynamic equations on time scales xΔ t a t x t h t , 1.5 xΔ t x0 , f t, x , with the initial condition x t0 are considered in 15 by Liu and Li The ... properties of the exponential function on time scales and obtain a sufficient and necessary condition that a t x t h t guarantees the existence of the periodic solutions of the equation xΔ t In 16 ,...

Ngày tải lên: 21/06/2014, 20:20

... second-order nonlinear dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol 318, no 2, pp 578–592, 2006 11 M Bohner and A Peterson, Dynamic Equations on Time ... Especially, Kaufmann and Raffoul considered a nonlinear functional dynamic equation on a time scale and obtained sufficient conditions for the existence of positive solutions, Li and Liu 10 studied the ... boundary conditions for ordinary differential equations and finite difference equations have been studied extensively, for example, see 1–4 and references therein However, there are not many concerning...

Ngày tải lên: 22/06/2014, 11:20

... differential equations established by the continuation method (see O’Regan and Precup [6]) are given in Chis [4, 7] ¸ Fixed Point Theory and Applications References [1] A Chis and R Precup, “Continuation ... Applications, vol of Series in Mathematical Analysis and Applications, Gordon and Breach Science, Amsterdam, The Netherlands, 2001 [7] A Chis, “Continuation methods for integral equations in locally ... theory for general contractions in gauge spaces,” Fixed ¸ Point Theory and Applications, vol 2004, no 3, pp 173–185, 2004 [2] M Frigon, “Fixed point results for generalized contractions in gauge spaces...

Ngày tải lên: 22/06/2014, 19:20