applications of second order differential equations in physics

... Properties of Solutions of Singular Second-Order Differential Equations Irena Rach ˚unkov ´a,1 Svatoslav Stan ˇek,1 Ewa Weinm ¨uller,2 1 Department of Mathematical Analysis, Faculty of Science, ... discontinuities at a discrete set of points in 0, T, compare 1 This study serves as a first step toward analysis of more involved nonlinearities, where typically, f has singular points also in ... discontinuous for certain values of the time variable t ∈ 0, T This form of f is motivated by a variety of initial and boundary value problems known from applications and having nonlinear,

Ngày tải lên: 21/06/2014, 20:20

... Article Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations Irena Rach ˚unkov ´a and Jan Tome ˇcek Department of Mathematical Analysis and Applications of Mathematics, ... This paper investigates the singular differential equation ptu ptfu, having a singularity at t  0 The existence of a strictly increasing solution a homoclinic solution satisfying u0 ... Therefore we will use the following definition Definition 1.3 A strictly increasing solution of problem 1.1, 1.2 is called a homoclinic solution. Numerical investigation of problem1.1, 1.2, where

Ngày tải lên: 21/06/2014, 20:20

... of solutions, which are different in the case (D) or (ND), in order totreat these cases simultaneously The classesW(Ω) are introduced inDefinition 2.1 atthe beginning ofSection 2 In the rest ofSection ... smoothness of the given data Such kind of estimatesinclude different versions of the maximum principle, which are crucial for investigation solu-of boundary value problems for second-order elliptic ... equations More icate properties of solutions, such as H¨older estimates and Harnack inequalities, are veryessential for the building of general theory of nonlinear equations (see [1–6]) del-In

Ngày tải lên: 22/06/2014, 22:20

... Article Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions Chao Zhang and Shurong Sun School of Science, University of Jinan, Jinan, Shandong ... Section 2 gives some preliminaries including existence and numbers of eigenvalues of the coupled boundary value problems, and some properties of eigenvalues of a kind of separated boundary value ... problems for second-order difference equations Existence of eigenvalues is proved, numbers of their eigenvalues are calculated, and their relationships between the eigenvalues of second-order difference

Ngày tải lên: 21/06/2014, 20:20

... 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 ... Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales Chao Zhang and Shurong Sun School of Science, University of Jinan, Jinan, Shandong 250022, China Correspondence should ... distribution, and reproduction in any medium, provided the original work is properly cited 1 Introduction In this paper, we consider the following second-order linear equations:  p1txΔtΔ q1tx

Ngày tải lên: 21/06/2014, 20:20

... bound-ary conditions containing this operator have been considered in [2,5] In [8], Man´asevich and Mawhin investigated the existence of periodic solutions to some system cases involving the fairly general ... distribution, and reproduction in any medium, provided the original work is properly cited 1 Introduction In recent years, the existence of periodic solutions for second-order Li´enard equations u + f (u, ... Recently, in [16] we studied the existence of periodic solutions for the nonlinear dif-ferential equation with ap-Laplacian-like operator  φ(u ) Hindawi Publishing Corporation Journal of Inequalities

Ngày tải lên: 22/06/2014, 22:20

... problems having more deviating arguments Also an example and graphs of numerical approximations ofyn,znare given InSection 6, we combined results of this paper with corresponding results of [4].Example ... elements of sequences { y n,z n } Using numerical methods we can find numerical approximations yn,znofy n,z n, respectively The graphs of someyn,zn are given inFigure 3.1 InSection 4, we investigate ... corresponding functions instead of constants Note that the special case whenf is monotone nonincreasing (with respect to the last two variables) is not discussed in paper [4] and is of particular interest

Ngày tải lên: 22/06/2014, 22:20

... functions f (x , y ) and ∂f∂y be continuous in some rectangle α < x < β, γ < y < δ containing the point (x0, y0) Then, in someinterval (x0− h, x0+ h) contained in (α, β), there is a unique ... functions f (x , y ) and ∂f∂y be continuous in some rectangle α < x < β, γ < y < δ containing the point (x0, y0) Then, in someinterval (x0− h, x0+ h) contained in (α, β), there is a unique ... functions f (x , y ) and ∂f∂y be continuous in some rectangle α < x < β, γ < y < δ containing the point (x0, y0) Then, in someinterval (x0− h, x0+ h) contained in (α, β), there is a unique

Ngày tải lên: 23/04/2020, 08:00

... 6Substituting2.21 into 1.1 yieldsTrang 7From2.29 and taking into account 2.27, we getMultiplying both sides of2.32 by H2σt, a1 and integrating both sides of the resulting inequality ... recently extended to second-order dynamic equations in 6 10 on oscillatory and nonoscillatory behavior of the second order nonlinear dynamic equations on time scales can be found in 11–23 Therefore, ... of Second-Order Mixed-Nonlinear Delay Dynamic Equations M ¨ Unal1 and A Zafer2 1 Department of Software Engineering, Bahc¸es¸ehir University, Bes¸iktas¸, 34538 Istanbul, Turkey 2 Department of

Ngày tải lên: 21/06/2014, 18:20

... is obtained for1.13 over a specific range of parameters and for initialconditions in an invariant compact interval.Theorem 1.4is proved inSection 5, and the proof ofTheorem 1.5is given inSection ... the signs of the partial derivatives of f x, y are constant on the interior of each of the setsm, M × m, K1 and m, M × K1, M, as shown inFigure 1 Since fx, y is nonincreasing in both ... solutions if either q ≥ 1 or p ≤ 1 By eliminating denominators in both equations in4.5, m − mM  Mp − M2q  r  0, and by subtracting terms in4.6 one obtains Since m /  M, we have qm  M  p

Ngày tải lên: 21/06/2014, 20:20

... reproduction in any medium, provided the original work is properly cited 1 Introduction This paper is concerned with study of nonoscillation of solutions of third-order nonlinear differential equations of ... differential equations,” Bulletin of the Institute of Mathematics Academia Sinica, vol 22, no 3, pp 267–274, 1994. 16 N Parhi and S Padhi, “On oscillatory linear differential equations of third order,” ... nonlinear third order differential equations,” Bulletin of the Institute of Mathematics Academia Sinica, vol 13, no 4, pp 367– 384, 1985 20 N Parhi and S Parhi, “On the behaviour of solutions of

Ngày tải lên: 22/06/2014, 02:20

... Applications, vol 39, no 2, pp 207–215, 2000. [7] D Bai and Y Xu, “Nontrivial solutions of boundary value problems of second-order difference equations,” Journal of Mathematical Analysis and Applications, ... has a solution provided b+1  The analogue ofTheorem 1.4was obtained for two-point BVPs of second-order or-dinary differential equations by Iannacci and Nkashama [2] Our paper is motivated by ... corresponding to any such eigenvalue is one dimen-sional The following lemma is crucial to the study of nonlinear perturbations of the linear problem (1.1) The required results are somewhat scattered in

Ngày tải lên: 22/06/2014, 19:20

... −1(−b/2) is an even multiple of π. 1 Introduction In this paper, we study the existence of periodic solutions of nonlinear, second-order, discrete time equations of the form y(t + 2) + by(t + ... second component function ofG maps each boundary point of Ω into Ω itself and then, by breaking up the boundary of Ω into separate pieces, consider the effect of the first component function of ... 1DIFFERENCE EQUATIONSJES ´US RODRIGUEZ AND DEBRA LYNN ETHERIDGE Received 6 August 2004 We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of

Ngày tải lên: 23/06/2014, 00:20

... that with these values of q f p the coefficients o f Wjqp in (2.8) are equal to zero Therefore, equating the coefficients o f sin <ỉ>5, c o s 0 5 in (2.8) we o b ta in : ị* f F 0 e ... r m o n ic s sin (ps, cos (ps in correspond to qs = ± 1 , q j = 0 (j 4= s) W ith th ese values o f q the coef­ ficient o f u lg in (1.13) is equal to zero Therefore, c o m p a r in g the coefficients ... Trang 62 NON-AUTONOMOUS EQUATION This p a r a g r a p h is devot ed to study of the differential equation of form (2 1 ) x iN) + a xx (N l) + + a N- ị i + ocNx = eF(x> X, X(N ), 0 l$ 0 r,

Ngày tải lên: 08/04/2015, 15:36

... continuation method of Mawhin [4], One of important hypotheses of Mawhin’s continuation theorem that is the Fredholm of index zero property of linear operator L which mean that (i) kerL has finite ... property, second order differential operator, continuation theorem, projector, generalized inverse 2010 MSC: 34B10, 34B15 1 Introduction The question of the solvability for nonlinear pertubation of differential ... Fredholm property of the operator L In the rest of paper we use the following notations  O is zero matrix of order d × d and θ is zero element of R d  Id : the identity matrix of order d.  Iν

Ngày tải lên: 14/10/2015, 08:45

... nicepresentation of methods as well as results in the area In recent years, there has been an increasing interest in extending certain classical results to differential equations in Banach spaces In this ... abstract functional differential equations with infinitedelay, there are three kinds of definitions of stabilities In Sections 3 and 4, we provesome equivalence of these definitions of stabilities ... the case of almost periodic solutions of (linear and nonlinear)equations in Banach spaces To this end, in the first chapter we present introduc-tions to the theory of semigroups of linear operators

Ngày tải lên: 29/10/2015, 12:32

... variation-of-constants formula in the theory of linear ordinary differential equations So, we often call the representation formula obtained here the variation-of-constants formula in the phase space Such ... is finite dimensional, the representation formula for functional differential equations has been established by Hale [5] in the case of finite delay and by Murakami [16] in the case of infinite ... admissibility of some spaces of functions whose spectra are contained in a closed subset of the real line © 2002 Elsevier Science Key Words: functional differential equations; phase space; variation-of-constants

Ngày tải lên: 17/12/2017, 16:49

... solving a linear algebraic system of equations The boundary value problem for the second-order differential equations, by the three-point difference method, leads soving of the system of equations ... methods For nonlinear equations, the use of approximation methods is almost inevitable In solving differential equations for differential equations, one can find their exact solutions in a very small ... Continuing the developent of the techniques in Chapter 2, in Chapter 3, for the system of coupled fully or non-fully nonlinear fourth-order differential equations, we also obtain the results of

Ngày tải lên: 01/04/2021, 19:17

... soon. Lyapunov-type inequalities for a class of even -order differential equations Journal of Inequalities and Applications 2012, 2012:5 doi:10.1186/1029-242X-2012-5 Qi-Ming Zhang (zhqm20082008@sina.com) Xiaofei ... below). For information about publishing your research in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information ... (2.11) Since |x(c)| > 0, divided the last inequality of (2.11) by |x(c)|, we can obtain (2.10).  By a similar method in the proof of Theorem 1.1, applying Lemmas 2.1 and 2.3, we can obtain the...

Ngày tải lên: 20/06/2014, 21:20

... k ≥ a In this case, completely analyzed in 1, any positive solution y is either decreasing or eventually increasing. We say that y is of class M  in the first case, of class M − in the second one. ... difference tending to zero, have two possible asymptotic behaviors, since they can be slowly varying or regularly varying with index 1 in case ii, or regularly varying with two different indices in case ... solutions of 1.1 and D denote the set of all positive dominant solutions of 1.1.FromTheorem 4.1, taking into account Theorem 3.1, the following characterization of recessive and dominant solution...

Ngày tải lên: 21/06/2014, 11:20