surveying second and higher order differential equations

... fourth-order differential equations into two forms: fully order differential equations and non-fully fourth-order ones A fourth-fourth-order differential equation whose right-hand side function contains ... mechanics and some other fields are described by differential equations or systems of differential equations with different bound-ary conditions It is possible to classify the fourth-order differential ... function and its derivatives of all order (from first to third order) is called a fully fourth-order differential equation Otherwise, the equation is called a non-fully fourth-order differential

Ngày tải lên: 01/04/2021, 19:17

... calculus of variations and nonlinear partial differential equations The list of speakers and the titles of lectures have been the following: - Luigi Ambrosio, Transport equation and Cauchy problem ... to fully nonlinear equations in ergodic random media It is mainlybased on the joint paper with Panagiotis Souganidis and Lihe Wang We will try to point out the main techniques and the common aspects.The ... in addition that f is 1-1 and onto and that |Jf| > 0 L d -a.e on A we can set A = f −1 (B) and g = ρ/ |Jf| to obtain In our case f (x) = X(t, x) is surely 1-1, onto and Lipschitz It remains

Ngày tải lên: 04/03/2019, 11:11

... Trang 1Infinite Series and Differential EquationsNguyen Thieu Huy Hanoi University of Science and Technology Trang 23.3 Solution: To solve Equation (1), first solve the equationsTrang 33.4 Integrating ... (C) To establish the (differential) equations. Analysis of the Model (A) To solve equations (B) To find the properties of solutions (C) If it is too difficult to solve the equations, try to approximate ... variables. (C) To establish the (differential) equations. (A) To solve equations (B) To find the properties of solutions (C) If it is too difficult to solve the equations, try to approximate the

Ngày tải lên: 23/04/2020, 08:00

... stands at 8 while your credence stands at 2 At time t1, you and I meet and compare notes How, if at all, should we revise our respective opinions? According to The Equal Weight View, you and ... possesses higher order evidence that suggests that the bearing of the original, first order evidence is something other than what one initially took it to be Moreover, this is so even if the higher order ... to the first order evidence and one’s peers have not The tendency of higher order considerations to affect how much confidence one should invest in the deliverances of one’s first order reasoning

Ngày tải lên: 18/10/2022, 14:32

... gestations and improving outcomes, none has had a substantial effect The purpose of this document is to review the issues and complications associated with twin, triplet, and higher-order multifetal ... of fetal and neonatal mortality, as well as morbidities, such as fetal and congenital anomalies, prematurity, and fetal growth restriction (11, 12) This trend also is seen in higher-order multifetal ... is recommended and should be initiated between 12 and 28 weeks of gestation (optimally before 16 weeks of gestation) and continued daily until delivery (24) Women with higher-order multifetal

Ngày tải lên: 06/03/2024, 09:41

... of second order, ordinary differential equations and special functions Trang 11Second-order ordinary differential equations11 List of Equations This is a list of the types of equation, and ... Trang 1Second-order ordinary differential equations Special functions, Sturm-Liouville theory and transforms Download free books at Trang 2R.S JohnsonSecond-order ordinary differential equations ... www.discovermitas.com Trang 8Second-order ordinary differential equations Contents3.4 Applications to the solution of differential and integral equations 147 Tables of a few standard Integral Transforms

Ngày tải lên: 13/01/2021, 09:54

... constructing upper and lower boundaries and using Leray-Schauder degree theory, we present a result about the existence and uniqueness of a periodic solution for second-order ordinary differential equations ... pagesdoi:10.1155/2011/192156 Research Article Existence and Uniqueness of Periodic Solution for Nonlinear Second-Order Ordinary Differential Equations Jian Zu College of Mathematics, Jilin University, ... ordinary differential equations is a very important branch in the differential equation theory Many results about the existence of periodic solutions for second-order differential equations have been

Ngày tải lên: 14/07/2023, 09:44

... delay differential equations of higher order for p(t) = ± 1 Arch Math 40, 359–366 (2004) 16 Tang, S, Li, T, Thandapani, E: Oscillation of higher-order half-linear neutral differential equations ... criteria for second-order superlinear neutral differential equations Abstr Appl Anal 2011, 1 –17 (2011) 13 Li, T, Han, Z, Zhao, P, Sun, S: Oscillation of even-order neutral delay differential equations ... Functional Differential Equations Marcel Dekker, New York (1995) 9 Karpuz, B, Öcalan, Ö, Öztürk, S: Comparison theorems on the oscillation and asymptotic behavior of higher-order neutral differential equations

Ngày tải lên: 20/06/2014, 22:20

... integral boundary conditions of fourth-order impulsive differential equations: k represent the right-hand limit and left-hand limit of xt at t  tk , respectively, and g, h ∈ L10, 1 is nonnegative. ... {θ} × P \ {θ} → P are continuous and may be singular at t  0, 1, u  0, and u  0; ai , b i , c i, and d i ∈ 0, ∞, and ρi  ai c i  ai d i  bi c i > 0, and m i , n i ∈ L10, 1 are nonnegative, ... corresponding to clamped and hinged ends and manynonlocal boundary conditions and established excellent existence results for multiple positivesolutions of fourth-order nonlinear equations which model

Ngày tải lên: 21/06/2014, 16:20

... Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument Li Wang and Chuanyi Zhang Department of Mathematics, Harbin ... properly cited 1 Introduction and Some Preliminaries Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener1 and Shah and Wiener 2, combine properties ... properties of both differential and difference equations and usually describe hybrid dynamical systems and have applications in certain biomedical models in the work of Busenberg and Cooke3 Over the years,

Ngày tải lên: 21/06/2014, 20:20

... 507671, 25 pagesdoi:10.1155/2009/507671 Research Article First-Order Singular and Discontinuous Differential Equations Daniel C Biles1 and Rodrigo L ´opez Pouso2 1 Department of Mathematics, Belmont ... greatest and the smallestCarath´eodory solutions for1.1 between given lower and upper solutions and assuming the existence of a L1-bound for f on the sector delimited by the graphs of the lower and ... I and satisfies l∗supt0  x0and l∗supt  ft, l∗ supt for a.a t ∈ I \ K, where K ∪n,m∈NK n,m and for all n, m ∈ N the set contains no positive measure set. Note that if the sets J n,m and

Ngày tải lên: 21/06/2014, 20:20

... doi:10.1155/2009/540863 Research Article Recent Existence Results for Second-Order Singular Periodic Differential Equations Jifeng Chu 1, 2 and Juan J. Nieto 3 1 Department of Mathematics, College of Science, ... essentially from 35 , and the results for. .. of Differential Equations, vol 232, no 1, pp 277–284, 2007 28 P J Torres, Existence and stability of periodic solutions for second-order semilinear ... of second order differential equation x   a  t  x  f  t, x   e  t  , 1.1 where at,et are continuous and T-periodic functions. The nonlinearity ft, x is continuous in t, x and

Ngày tải lên: 21/06/2014, 20:20

... pagesdoi:10.1155/2008/389028 Research Article On Periodic Solutions of Higher-Order Functional Differential Equations I Kiguradze, 1 N Partsvania, 1 and B P ˚u ˇza 2 1 Andrea Razmadze Mathematical Institute, 1 Aleksidze ... O’Regan For higher-order functional differential equations and, particularly, for nonautonomous differential equations with deviated arguments, new sufficient conditions for the existence and uniqueness ... function h : 0, ∞→ 0, ∞ and constants c ≥ 0, ik ≥ 0 i  1, 2; k  1, , n − 1,  ≥ 1, and σ ∈ {−1, 1} such that hx → ∞ as x → ∞, n−1  k1 and inequalities1.11 and 1.12 are satisfied

Ngày tải lên: 21/06/2014, 22:20

... D R Anderson, “Solutions to second- order three-point problems on time scales,” Journal of Difference Equations and Applications, vol 8, no 8, pp 673–688, 2002 D R Anderson and I Y Karaca, Higher- order ... using Krasnosel’skii fixed point theorem Recently, Anderson and Karaca studied higher- order three-point boundary value problems on time scales and obtained criteria for the existence of positive ... 2004 14 J A Gatica, V Oliker, and P Waltman, “Singular nonlinear boundary value problems for secondorder ordinary differential equations, ” Journal of Differential Equations, vol 79, no 1, pp 62–78,...

Ngày tải lên: 21/06/2014, 20:20

... 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 ... Functional differential equations with state-dependent delays: theory and applications Handbook of Differential Equations: Ordinary Differential Equations, vol III Elsevier/North-Holland, Amsterdam (2006), ... all t ∈ I− and β (t) = m ≥ max y≤maxI β(t) f (y) for all t ∈ I0 (25) So we deduce from (24) and (25) that α and β are lower and upper solutions for problem (13) Rub´n Figueroa∗ and Rodrigo...

Ngày tải lên: 20/06/2014, 20:20

... k, and M Tvrdy, “Singularities and Laplacians in boundary value problems a e ˚ ´ for nonlinear ordinary differential equations, ” in Handbook of Differential Equations: Ordinary a Differential Equations, ... satisfies 3.29 for a ∈ −1, and a < −1, and 3.32 for a −1 We first note that, by 3.9 , for all a < 0, Therefore, c2 values, ⇐⇒ c2 lim u t u t→0 3.39 in both, 3.29 and 3.32 , and the result now follows ... Problems 15 for a.e t ∈ 0, T and all x1 , y1 , x2 , y2 ∈ K Then problem 5.1a and 5.1b has at most one solution Proof Let u1 and u2 be different solutions of problem 5.1a and 5.1b Since u1 , u2 ∈...

Ngày tải lên: 21/06/2014, 20:20

... local maximum between the first and the second zero, then just one negative local minimum between the second and the third zero, and so on By 3.8 , 3.9 , 1.4 – 1.6 and 1.13 , these maxima are decreasing ... t < L for t ∈ a1 , b and consequently f u t f u t for t ∈ a1 , b By 4.23 and 2.26 , f u t < on a1 , b and thus p t u t and u t are negative on a1 , b So, u is positive and decreasing on a1 ... possibilities b < ∞ and b ∞ can occur Let b ∞ We write Let b < ∞ By Theorem 4.4 and Lemma 2.5, u b ∈ 0, L , u b limt → ∞ u t Using Lemmas 3.5 and 2.5 and Theorem 4.4, we u b limt → ∞ u t , u b and either...

Ngày tải lên: 21/06/2014, 20:20

... Journal of Computational and Applied Mathematics 136 (2001), no 1-2, 189–197 [7] D Jiang and J Wei, Monotone method for first- and second- order periodic boundary value problems and periodic solutions ... differential equations, Nonlinear Analysis 50 (2002), no 7, 885–898 [8] D Jiang, P Weng, and X Li, Periodic boundary value problems for second order differential equations with delay and monotone ... problems for second order differential equations [4] with deviating arguments, Journal of Mathematical Analysis and Applications 312 (2005), no 2, 620–636 , Boundary value problems for first order differential...

Ngày tải lên: 22/06/2014, 22:20

... uniformly and monotonically to the unique solution of (1.1), and the convergence is of order T G Melton and A S Vatsala Preliminaries In this section, we recall some well known theorems and corollaries ... nonincreasing and fu + gu < on Ω Then there exist monotone sequences {αn (t)} and {βn (t)}, n ≥ which converge uniformly and monotonically to the unique solution of (3.1) and the convergence is of order ... ≤ αn+1 ≤ βn+1 ≤ βn on J, where αn+1 and βn+1 are solutions of BVPs (3.6) and (3.7), respectively, with α = αn and β = βn The inequalities (3.2) and (3.4), and (3.15) imply −αn ≤ f t,αn + g t,αn...

Ngày tải lên: 22/06/2014, 22:20

... Ordinary Differential Equations and Differential- Algebraic Equations SIAM Berz, M (1999) Modern Map Methods in Particle Beam Physics Academic Press, San Diego Berz, M (2000) Higher order veried ... more general higher order ODEs 3.1 Example Earlier, we indicated that the presented method can also be used for the direct integration of higher order problems To illustrate this, and to show ...    be open and assume that Denition Let we say that equals up to order if partial derivatives of orders up to agree at the origin If order , we denote that by For equals and all up to $...

Ngày tải lên: 12/01/2014, 21:46