second order linear ordinary differential equation with variable coefficients

... 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...

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... 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...

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... Difference Equations Volume 2009, Article ID 143175, 14 pages doi:10.1155/2009/143175 Research Article On the Spectrum of Almost Periodic Solution of Second- Order Neutral Delay Differential Equations with ... 14 Advances in Difference Equations 12 R. Yuan, “On the spectrum of almost periodic solution of second- order differential equations with piecewise constant argument,” Nonlinear Analysis: Theory, ... difference equations with piecewise constant arguments,” Acta Mathematica Sinica, vol. 18, no. 2, pp. 263–276, 2002. 6 H X. Li, “Almost periodic solutions of second- order neutral delay-differential equations...

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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 ... 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...

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... 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...

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... Difference Equations 8 J. Shao and F. Meng, “Oscillation theorems for second- order forced neutral nonlinear differential equations with delayed argument,” International Journal of Differential Equations, ... for second- order forced dynamic equations with mixed nonlinearities,” Advances in Difference Equations, vol. 2009, Article ID 938706, 20 pages, 2009. 11 C. Li and S. Chen, “Oscillation of second- order ... forced second- order mixed type quasilinear delay differential equations,” Electronic Journal of Differential Equations, p. No. 73, 9, 2010. 13 Y. G. Sun and F. W. Meng, “Oscillation of second- order...

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... 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...

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... 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...

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... 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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... Differential Equations, vol. 232, no. 1, pp. 277–284, 2007. 28 P. J. Torres, “Existence and stability of periodic solutions for second- order semilinear differential equations with a singular nonlinearity,” ... singularity,” Advanced Nonlinear Studies, vol. 7, no. 4, pp. 629–649, 2007. 24 J. Chu and M. Li, “Positive periodic solutions of Hill’s equations with singular nonlinear perturbations,” Nonlinear Analysis: ... in Nonlinear Differential Equations and Their Applications, 10, Birkh ă auser, Boston, Mass, USA, 1993. 17 A. C. Lazer and S. Solimini, “On periodic solutions of nonlinear differential equations with singularities,”...

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... differential equations with variable delays,” Nonlinear Analysis, vol. 63, no. 5–7, pp. e233–e242, 2005. 8 V. B. Kolmanovskii and L. E. Shaikhet, “Matrix Riccati equations and stability of stochastic linear systems ... asymptotic stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary Meng Wu ... stability of a generalized linear neutral stochastic differential equation with variable delays by using the fixed point theory. An asymptotic mean square stability theorem with a necessary and sufficient...

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... variational methods when we solve super- linear differential equations such as elliptic problems, Dirac equations, Hamiltonian systems, wave equations, and Schrödinger equations. Theorem 3.2. Assume that ... solutions for p(x)-Laplacian equations in ℝ N . Nonlinear Anal. 59, 173–188 (2004) 19. Rabinowitz, PH: Minimax methods in critical point theory with applications to differential equations. In CBMS Reg ... 2011:33 http://www.boundaryvalueproblems.com/content/2011/1/33 Page 10 of 15 RESEARC H Open Access Infinitely many periodic solutions for some second- order differential systems with p(t)- Laplacian Liang Zhang, Xian Hua Tang * and Jing Chen * Correspondence: mathspaper@126.com School...

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... 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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... 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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