... study a class of nonlocalBVPs for nth -order impulsive differential equations with fixed moments.Consider the following nth -order impulsive differential equations with integralboundary conditions:xnt ... pagesdoi:10.1155/2011/456426Research ArticlePositive Solutions of nth -Order NonlinearImpulsive DifferentialEquationwith NonlocalBoundary ConditionsMeiqiang Feng,1Xuemei Zhang,2and Xiaozhong ... problem for secondorder ordinary differentialequations,” Applied Mathematics and Computation, vol. 89, no. 1–3, pp. 133–146, 1998.29 W. Feng, “On an m-point boundary value problem,” Nonlinear...
... 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 ... pagesdoi:10.1155/2011/720702Research ArticleNew Existence Results for Higher -Order Nonlinear Fractional DifferentialEquation with Integral Boundary ConditionsMeiqiang Feng,1Xuemei Zhang,2, 3and ... class of higher- order nonlinear fractional differential equations with integral boundary conditions. The resultsare established by converting the problem into an equivalent integral equation and...
... the solutions beingoscillating for a class of linear second- order delayed-discrete equations.We consider the delayed second- orderlinear discrete equation Δxn −pnxn − 1, 1.1where ... original work is properly cited.A linear second- order discrete-delayed equation Δxn−pnxn − 1 with a positive coefficientp 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...
... kind of second- order rational difference equation. With the change of the initial values, we find thesuccessive lengths of positive and negative semicycles for oscillatory solutions of this equation, ... RESEARCH Open AccessOn a class of second- order nonlinear difference equation Li Dongsheng1*, Zou Shuliang1and Liao Maoxin2* Correspondence: lds1010@sina.com1School ... stabilityTheorem 3.5. The positive equilibrium point of Equation (1.1) is locally asymptoticallystable.Proof. The linearized equation of Equation (1.1) about the positive equilibrium point¯xisyn+1=0·yn+0·yn−1,...
... investigates the existence of apositive solution for a class of nonlinear boundary value problems of second- order differential equations with integral boundary conditions in abstract spaces. Thearguments ... for secondorder impulsive differential equations. J Math AnalAppl. 331(1), 159–176 (2007). doi:10.1016/j.jmaa.2006.07.1066. 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) =10g(t)x(t)dt, x(1) = θ .Let E be a real Banach space with norm || · || and...
... 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 EquationsVolume 2011, Article ID 546038, 14 pagesdoi:10.1155/2011/546038Research ArticleThe Existence of Positive Solution toa Nonlinear Fractional Differential Equation with Integral ... fractionaldifferential 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 fractionaldifferential...
... solutions to second orderlinear 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- orderLinear ... supn{n2|an−a0−a1/n−ln|} is a constant. Equation 4.14 is an inhomogeneous second- orderlinear difference equation; its solution takes theform of a particular solution added to an arbitrary linear combination ... “summary equation 2.1. Next weconsider a nonlinear first -order difference equation. 2 Advances in Difference EquationsUnlike t he method used by Olver 4 to treat asymptotic solutions of second- order linear...
... solutions of two-point boundary value problems for systemsof 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 forproblem P with two-point boundary condition. Let us consider the following second- order impulsive ... and multiplicity of positive solutions of a singular boundaryvalue problem for second- order differential systems with impulse effects. By using the upper andlower solutions method and fixed point...
... cited.The nonlinear alternative of the Leray Schauder type and the Banach contraction principle areused to investigate the existence of solutions for second- order differential equations with integralboundary ... Brykalov, “A secondorder nonlinear problem with two-point and integral boundaryconditions,” Georgian Mathematical Journal, vol. 1, pp. 243–249, 1994.11 M. Denche and A. L. Marhoune, “High order ... for secondorder nonlinearsingular 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...
... for secondorder impulsivedifferential 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 secondorder nonlinearsingular differential equations,” Georgian Mathematical Journal, vol. 7, no. 1, pp. 133–154, 2000.22 C. Corduneanu, Integral Equations and Applications, ... with integral boundary conditionsand one-dimensional p-Laplacian,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 9,pp. 3119–3126, 2009.19 J. M. Gallardo, Second- order...
... 0 (such as BVP (1.1)) with b = 0. It is a well-knownfact that the boundary value problems with Sturm–Liouville boundary value conditionsfor integral order differential equations have important ... (1.5). Secondly, whenα = 2, β = 1, γ = 1, then BVP (1.5) reduces to BVP (1.2) with b = 0. So, BVP (1.5) isan important generalization of BVP (1.2) from integral order to fractional order. Thirdly,in ... articles dealing with the existence of solutions to boundaryvalue problems for fractional differential equationwith p-Laplacian operator. In [24], theauthors investigated the nonlinear nonlocal...
... for secondorder nonlinear differentialequations,” 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: μt ≡ 1. This result is the same as Sturm comparison theoremof second- order difference equations ... of second- orderlinear equations on timescales. 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...