linear differential equations with constant and variable coefficients

Ngày tải lên: 22/03/2014, 11:20

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 23/06/2014, 00:20

Ngày tải lên: 21/06/2014, 23:20

Ngày tải lên: 22/06/2014, 22:20

... solutions to linear differential equations and systems of equations exemplify important ideas in linear algebra, and how linear algebra often answers key questions regarding differential equations. ã ... solutions to systems of linear differential equations or higher order linear differential equations. Over the past decade or two, first-order differential equations have become a standard topic that ... array (called a matrix) and eliminate the redundancy of repeatedly writing the variables. Let us reconsider Differential Equations with Linear Algebra Systems of linear equations 13 1 2 1 3 2 x 2 x 1 x 3 Figure...

Ngày tải lên: 11/06/2014, 07:16

Ngày tải lên: 12/06/2014, 16:17

... Functional differential equations with state-dependent delays: theory and applications. Hand- b ook of Differential Equations: Ordinary Differential Equations, vol. III. Elsevier/North-Holland, Amsterdam ... Remark 2, the lower solution α and the upper solution β satisfy, respectively, inequalities (7) and (8) and, conversely, if α and β satisfy (7) and (8) then they are lower and upper solutions in the ... required for the functions f and τ, and they need not be continuous with respect to their first variable. This article is organized as follows. In Section 2, we state and prove the main results...

Ngày tải lên: 20/06/2014, 20:20

... neutral nonlinear differential equations with delay. Nonlinear Anal. 74(12):3926–3933 (2011). doi:10.1016/j.na.2011.02.029 17. Raffoul, YN: Stability in neutral nonlinear differential equations with ... points and stability in neutral differential equations with variable delays. Proc Am Math Soc. 136, 909–918 (2008) 19. Ardjouni, A, Djoudi, A: Fixed points and stability in linear neutral differential ... Then, together with Sakthivel and Luo [11,12] investigate the asymptotic stability of the non- linear impulsive stochastic differential equations and the impulsive stochastic partial differential equations...

Ngày tải lên: 20/06/2014, 22:20

Ngày tải lên: 21/06/2014, 16:20

Ngày tải lên: 21/06/2014, 20:20

... τ  )=1,thenA τ ⊆A τ  . (iv) The random variables τ ∧τ  , τ ∨ τ  and (τ + τ  ) are stopping times. (v) If for a real valued random variable Y we have E(|Y |) < ∞ and P (τ ≤ τ  )=1,then E(Y |A τ )=E(Y ... in- tegrals such as the linearity property E  αX + βY   S  = αE  X   S  + βE  Y   S  , (1.1.13) where X and Y are integrable random variables and α, β ∈are deterministic constants. Furthermore, ... quantitative analysts and others with a more technical back- ground in mathematical and quantitative methods who are interested in applying stochastic differential equations with jumps, and in implement- ing...

Ngày tải lên: 19/02/2014, 22:20

Ngày tải lên: 14/03/2014, 13:20

Ngày tải lên: 31/03/2014, 15:56

... to a K -linear map 1 K ⊗f : K ⊗ k A → K ⊗ k B,which commutes with ∂. Therefore f induces a C -linear map S(f ):S(A) → S(B) with commutes with the G-actions. We will omit the straightforward and tedious ... A 0 Y with A 0 ∈ M n (C) and such that the distinct eigenvalues of A 0 do not differ by integers. Proof. We begin with a well known fact from linear algebra. Let U, V ∈ M n (C) and assume that U and ... a constant if c  =0. ✷ In Exercise 1.5.1, the reader is asked to show that the set of constants in a ring forms a ring and in a field forms a field. The ring of constants in Exam- ples 1.2.1 and...

Ngày tải lên: 31/03/2014, 15:56

Ngày tải lên: 12/06/2014, 16:16

... Physics and Engineering. Springer, Dordrecht (2007) 3. Agarwal, RP, Andrade, B, Cuevas, C: Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations. Nonlinear ... higher-order nonlinear fractional differential equations. Fixed Point Theory Appl 2010, 17 (2010). (Article ID 364560) 10. Ahmad, B, Nieto, JJ: Riemann-Liouville fractional differential equations with fractional ... solution for fractional differential equations with uncertainty. Nonlinear Anal. 72, 2859–2862 (2010). doi:10.1016/j.na.2009.11.029 5. Ahmad, B, Nieto, JJ: Existence results for nonlinear boundary value...

Ngày tải lên: 20/06/2014, 22:20

... On some nonlinear ordinary differential equations with advanced arguments. Nonlinear Anal 2003, 53:495-505. 40. Yan JR: Oscillation of first-order impulsive differential equations with advanced ... order differential equations with an advanced argument. Nonlinear Anal 2006, 65:2013-2023. 42. Jankowski T: Positive solutions for fourth-order differential equations with deviating arguments and ... the subject of fractional differential equations is gaining much impor- tance and attention. For details, see [18-36] and the references therein. Differential equations with deviated arguments...

Ngày tải lên: 21/06/2014, 03:20

... pp. 143–150, 2008. 8 D. Qian and X. Li, “Periodic solutions for ordinary differential equations with s ublinear impulsive effects,” Journal of Mathematical Analysis and Applications, vol. 303, no. ... Mathematics and Computing, vol. 31, no. 1-2, pp. 255–265, 2009. 13 H. Zhang and Z. Li, “Variational approach to impulsive differential equations with periodic boundary conditions,” Nonlinear Analysis. ... theory 8, and the method of lower and upper solutions with monotone iterative technique 9 to study the existence of solutions for impulsive differential equations. On the other hand, in the...

Ngày tải lên: 21/06/2014, 11:20

... and Continuous Dynamical Systems. Series S, vol. 1, no. 1, pp. 89–97, 2008. 4 G. Infante and J. R. L. Webb, “Nonlinear non-local boundary-value problems and perturbed Hammerstein integral equations, ” ... Singular p-Laplacian Differential Equations with Integral Boundary Conditions Xingqiu Zhang 1, 2 and Yujun Cui 3 1 Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei ... 2.31 then from 2.29 and 2.30, we have 2.25. Lemma 2.5. Suppose that H holds. And assume that there exist lower and upper solutions of BVP 1.1, respectively, αt and βt, such that αt,βt...

Ngày tải lên: 21/06/2014, 11:20