homogeneous linear differential equations with constant coefficients

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... 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 ... general 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 ... Matrix exponential 270 4 Higher order differential equations 273 4.1 Motivating equations 273 4.2 Homogeneous equations: distinct real roots 274 4.3 Homogeneous equations: repeated and complex roots...

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... N = {N t ,t≥ 0} with intensity λ>0 is a piecewise constant process with stationary independent increments with initial value N 0 =0such that N t − N s is Poisson distributed with intensity λ t−s , ... approximation of SDEs with jumps represents the focus of the monograph. The reader learns about powerful numerical methods for the solution of SDEs with jumps. These need to be implemented with care. It ... 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...

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... on {α 1 , ,α n }. Exercises 1.14 1. Homogeneous versus inhomogeneous equations Let k be a differential field and L(y)=b,withb =0,ann th order inhomogeneous linear differential equation over k.Let L h (y)=b( 1 b L(y))  . (a) ... of linear differential equations (which we shall refer to simply as differential Galois theory) is the analogue for linear differential equations of the classical Galois theory for polynomial equations. ... morphism in {{M}}.Thenf extends 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...

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... HO, Wu, J: Functional differential equations with state-dependent delays: theory and applications. Hand- b ook of Differential Equations: Ordinary Differential Equations, vol. III. Elsevier/North-Holland, ... problems with state-dep endent deviating arguments Bull. Lond. Math. Soc. 43, 164–174 (2011) 2. Arino, O, Hadeler, KP, Hbid, ML: Existence of periodic solutions for delay differential equations with ... differential equations with deviated arguments. J. Optim. Theory Appl. 135(2), 257–269 (2007) 5. Jankowski, T: Existence of solutions of boundary value problems for dif- ferential equations in...

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... 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 ... 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 equations with variable ... stochastic differential equations with multi- ple delays. Pinto and Seplveda [16] talk about H-asymptotic stability by the fixed point method in neutral nonlinear differential equations with delay....

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... 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 ... integrodifferential equations with integral boundary conditions. Bound Value Probl 2009, 11 (2009). (Article ID 708576) 6. Ahmad, B, Nieto, JJ: Existence results for a coupled system of nonlinear...

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... for non -linear differential equations of fractional order. Nonlinear Anal 2011, 74:792-804. 34. Zhang L, Wang G: Existence of solutions for nonlinear fractional differential equations with impulses ... 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 ... for second 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...

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... ordinary differential equations with s ublinear impulsive effects,” Journal of Mathematical Analysis and Applications, vol. 303, no. 1, pp. 288–303, 2005. 9 L. Chen and J. Sun, “Nonlinear boundary ... 2009. 13 H. Zhang and Z. Li, “Variational approach to impulsive differential equations with periodic boundary conditions,” Nonlinear Analysis. Real World Applications, vol. 11, no. 1, pp. 67–78, 2010. 14 ... problem with impulses,” Nonlinear Analysis. Real World Applications, vol. 11, no. 1, pp. 155–162, 2010. 15 J. Zhou and Y. Li, “Existence and multiplicity of solutions for some Dirichlet problems with...

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... pages doi:10.1155/2010/862079 Research Article Positive Solutions for Fourth-Order Singular p-Laplacian Differential Equations with Integral Boundary Conditions Xingqiu Zhang 1, 2 and Yujun Cui 3 1 Department of ... positive solutions for fourth-order singular p-Laplacian differential equations with integral boundary conditions. Our nonlinearity f may be singular at t  0, t  1, and u  0. The dual results ... consider the existence of positive solutions for the following nonlinear fourth-order singular p-Laplacian differential equations with integral boundary conditions:  ϕ p  x   t     f  t,...

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... Difference Equations Volume 2010, Article ID 691721, 10 pages doi:10.1155/2010/691721 Research Article Existence of Solutions for Nonlinear Fractional Integro -Differential Equations with Three-Point Nonlocal ... on fractional differential equations, see 5–11 and the references therein. In this paper, we study the following nonlinear fractional integro-differential equations with three-point nonlocal ... higher- order nonlinear fractional differential equations, ” Abstract and Applied Analysis, vol. 2009, Article ID 494720, 9 pages, 2009. 14 B. Ahmad and J. R. Graef, “Coupled systems of nonlinear fractional...

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