second order linear differential equation with variable coefficients pdf

Ngày tải lên: 22/06/2014, 22:20

... investigates the existence of a positive solution for a class of nonlinear boundary value problems of second- order differential equations with integral boundary conditions in abstract spaces. The arguments ... for second order impulsive differential equations. J Math Anal Appl. 331(1), 159–176 (2007). doi:10.1016/j.jmaa.2006.07.106 6. Zhang, G, Sun, J: Multiple positive solutions of singular second- order ... theorem [10] i n cone to the second- order differential equations.  x  (t )+f (t, x(t)) = θ ,0< t < 1, x(0) =  1 0 g(t)x(t)dt, x(1) = θ . Let E be a real Banach space with norm || · || and...

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Ngày tải lên: 23/06/2014, 00:20

... study a class of nonlocal BVPs for nth -order impulsive differential equations with fixed moments. Consider the following nth -order impulsive differential equations with integral boundary conditions: x n  t   ... pages doi:10.1155/2011/456426 Research Article Positive Solutions of nth -Order Nonlinear Impulsive Differential Equation with Nonlocal Boundary Conditions Meiqiang Feng, 1 Xuemei Zhang, 2 and Xiaozhong ... problem for second order ordinary differential equations,” Applied Mathematics and Computation, vol. 89, no. 1–3, pp. 133–146, 1998. 29 W. Feng, “On an m-point boundary value problem,” Nonlinear...

Ngày tải lên: 21/06/2014, 16:20

... differential equations with fractional order and nonlocal conditions,” Nonlinear Analysis: Theory, Methods and Applications, vol. 71, no. 7-8, pp. 2391–2396, 2009. 17 H. A. H. Salem, “On the nonlinear ... pages doi:10.1155/2011/720702 Research Article New Existence Results for Higher -Order Nonlinear Fractional Differential Equation with Integral Boundary Conditions Meiqiang Feng, 1 Xuemei Zhang, 2, 3 and ... class of higher- order nonlinear fractional differential equations with integral boundary conditions. The results are established by converting the problem into an equivalent integral equation and...

Ngày tải lên: 21/06/2014, 16:20

... the solutions being oscillating for a class of linear second- order delayed-discrete equations. We consider the delayed second- order linear discrete equation Δx  n   −p  n  x  n − 1  , 1.1 where ... original work is properly cited. A linear second- order discrete-delayed equation Δxn−pnxn − 1 with a positive coefficient p is considered for n →∞. This equation is known to have a positive ... P. Agarwal and A. Zafer, “Oscillation criteria for second- order forced dynamic equations with mixed nonlinearities,” Advances in Difference Equations, vol. 2009, Article ID 938706, 20 pages, 2009. 2...

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Ngày tải lên: 22/03/2014, 11:20

... kind of second- order rational difference equation. With the change of the initial values, we find the successive lengths of positive and negative semicycles for oscillatory solutions of this equation, ... RESEARCH Open Access On a class of second- order nonlinear difference equation Li Dongsheng 1* , Zou Shuliang 1 and Liao Maoxin 2 * Correspondence: lds1010@sina. com 1 School ... stability Theorem 3.5. The positive equilibrium point of Equation (1.1) is locally asymptotically stable. Proof. The linearized equation of Equation (1.1) about the positive equilibrium point ¯ x is y n+1 =0· y n +0· y n−1 ,...

Ngày tải lên: 20/06/2014, 22:20

... 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 ... 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 ... neutral differential equation, variable delays 1 Introduction The objective of this article is to investigate the stability of the zero solution of the first -order linear neutral differential equations...

Ngày tải lên: 20/06/2014, 22:20

... Differential Equations, no. 36, pp. 1–12, 2006. 16 M. Benchohra, S. Hamani, and S. K. Ntouyas, “Boundary value problems for differential equations with fractional order and nonlocal conditions,” Nonlinear ... Difference Equations Volume 2011, Article ID 546038, 14 pages doi:10.1155/2011/546038 Research Article The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral ... fractional differential equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1345–1351, 2010. 24 M. Feng, X. Zhang, and W. Ge, “New existence results for higher -order nonlinear fractional diff erential...

Ngày tải lên: 21/06/2014, 05:20

... with Btβ. Since the parameters Bt is variable, we cannot expect to transform directly BVP1.2 into an integral equation as in 16. We will apply the cone fixed point theory, combining with the ... problems,” Nonlinear Analysis. Theory, Methods & Applications, vol. 67, no. 6, pp. 1704–1709, 2007. 3 G. Chai, “Existence of positive solutions for fourth -order boundary value problem with variable parameters,” ... value problem with a p-Laplacian,” Computers & Mathematics with Applications, vol. 58, no. 6, pp. 1103–1112, 2009. 16 Z. Bai, “Positive solutions of some nonlocal fourth -order boundary...

Ngày tải lên: 21/06/2014, 07:20

... solutions to second order linear difference equations in the first case. For the second case, we leave it to the second part of this paper: Error Bound for Asymptotic Solutions of Second- order Linear ... “summary equation 2.1. Next we consider a nonlinear first -order difference equation. 2 Advances in Difference Equations Unlike t he method used by Olver 4 to treat asymptotic solutions of second- order linear ... of the definitions of α i ,ρ i in 1.5, 1.7,and2p − q  1. Equation 3.8 is a second- order linear difference equation with two known linear independent solutions. Its coefficients are quite similar...

Ngày tải lên: 21/06/2014, 11:20

... solutions of two-point boundary value problems for systems of nonlinear second- order singular and impulsive differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, ... problem P with Dirichlet boundary condition and the existence and nonexistence part of the result for problem P with two-point boundary condition. Let us consider the following second- order impulsive ... and multiplicity of positive solutions of a singular boundary value problem for second- order differential systems with impulse effects. By using the upper and lower solutions method and fixed point...

Ngày tải lên: 21/06/2014, 11:20

... cited. The nonlinear alternative of the Leray Schauder type and the Banach contraction principle are used to investigate the existence of solutions for second- order differential equations with integral boundary ... Brykalov, “A second order nonlinear problem with two-point and integral boundary conditions,” Georgian Mathematical Journal, vol. 1, pp. 243–249, 1994. 11 M. Denche and A. L. Marhoune, “High order ... for second order nonlinear singular differential equations,” Georgian Mathematical Journal, vol. 7, no. 1, pp. 133–154, 2000. 7 J. R. L. Webb, “Positive solutions of some higher order nonlocal...

Ngày tải lên: 21/06/2014, 11:20

... for second order impulsive differential equations with advanced arguments,” Applied Mathematics and Computation, vol. 197, no. 1, pp. 179–189, 2008. 17 T. Jankowski, “Positive solutions to second ... boundary value problem for second order nonlinear singular differential equations,” Georgian Mathematical Journal, vol. 7, no. 1, pp. 133–154, 2000. 22 C. Corduneanu, Integral Equations and Applications, ... with integral boundary conditions and one-dimensional p-Laplacian,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 9, pp. 3119–3126, 2009. 19 J. M. Gallardo, Second- order...

Ngày tải lên: 21/06/2014, 16:20

... 0 (such as BVP (1.1)) with b = 0. It is a well-known fact that the boundary value problems with Sturm–Liouville boundary value conditions for integral order differential equations have important ... (1.5). Secondly, when α = 2, β = 1, γ = 1, then BVP (1.5) reduces to BVP (1.2) with b = 0. So, BVP (1.5) is an important generalization of BVP (1.2) from integral order to fractional order. Thirdly, in ... articles dealing with the existence of solutions to boundary value problems for fractional differential equation with p-Laplacian operator. In [24], the authors investigated the nonlinear nonlocal...

Ngày tải lên: 21/06/2014, 17:20

... for second order nonlinear differential equations,” Annals of Differential Equations, vol. 19, no. 3, pp. 480–486, 2003. 7 R K. Zhuang and H W. Wu, “Sturm comparison theorem of solution for second ... theorem of second- order differential equations see Section 1. Remark 3.6. In the discrete case: μt ≡ 1. This result is the same as Sturm comparison theorem of second- order difference equations ... of second- order linear equations on time scales. We first establish Picone identity on time scales and obtain our main result by using it. Also, our result unifies the existing ones of second- order...

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