application of second order differential equation in real life

... contraction mapping principle implies that A n0 has a unique fixed point x∗ in CI, and so  A has a unique fixed point x∗ in CI; by the definition of  A, A has a unique fixed point x∗ in CI, ... three-point BVPs, see 2 5, 10, 12 and references therein Recently, the existence of solutions of third-order three-point BVP1.1 has been studied in 2,3 Guo et al 2 show the existence of positive ... by using cone expansion-compression fixed point theorem In 3, the singular third-order three-point BVP1.1 is considered under some conditions concerning the first eigenvalues corresponding

Ngày tải lên: 21/06/2014, 05:20

... added] 0 min one m dA dA)/ ool L -1 of Binding Sites mol L Binding sites present in × − ( 1 ssystem fraction of added bound per system’s lim = = (min) ( dA 0 iiting binding rate) min 0 1 = − ... any value of A to distinguish it from the highest value of κ, when A → 0, giving κ 0 , the system's limiting binding rate. Thus, if κ 0 is increased, then the ligand binding increases and ... binding rate constant for one mole of binding sites evaluated at A → 0, where Γ fr → 1. It characterizes the binding strength of the ligand for the binding site. Therefore, a high value of k bind

Ngày tải lên: 13/08/2014, 16:20

... 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 Institute of ... Statement of Main Theorem We begin this section with a definition of the solution of1.1 Definition 2.1 A continuous function x : R → R is called a solution of 1.1 if the following conditions ... ω This brings more convenience to study the spectrum containment of almost periodic solution of1.1 Now, we are in the position to show the Main Theorem The proof of Main Theorem Since H1

Ngày tải lên: 21/06/2014, 20:20

... 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

... smoothness of the given data. Such kind of estimates include different versions of the maximum principle, which are crucial for investigation of boundary value problems for second-order elliptic ... classes of solutions, which are different in the case (D)or(ND), in order to treat these cases simultaneously. The classes W(Ω) are introduced in Definition 2.1 at the beginning of Section 2. In the ... compact support in Ω ∩ B 4r . By approx- imation, we can put φ 0 in place of φ in the inequality (2.1) corresponding to Lu ≤ 0inΩ, that is,   Dφ 0 ,aDu  dx ≤ 0. (2.18) Having in mind that Du ε

Ngày tải lên: 22/06/2014, 22:20

... asymptotics of the solutions. .. n→∞ (4.10) Thus, the limiting equation is exactly the linearized equation (4.1), and an application of Poincar´ ’s theorem completes the proof of the theorem ... are positive real numbers and the initial condi- tions x −1 , x 0 are arbitrary nonnegative real numbers. Related nonlinear second-order rational difference equations were investigated in [2 , 5, ... study of these equations is quite challenging and is in rapid devel- opment. In this paper, we will demonstrate the use of Poincar ´ e’s theorem and an improvement of Perron’s theorem to determine

Ngày tải lên: 23/06/2014, 00:20

... 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) ker has finite ... 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 ... Mawhin, Coincidence Degree and Nonlinear Differential Equations, vol 568, Lecture Notes in Math., Springer-Verlag, Berlin, 1977 [5] C P Gupta, Existence theorems for a second order m-point

Ngày tải lên: 14/10/2015, 08:45

... f differential equations of tria n g u la r fo r m and those, o f truncated differential equations I Introduction Let us consider in a given separable Hilbert space // differential equations of ... conditions of global theorem on the existence and uniqueness of solutions (see e.g p 187-189]) An interesting problem studied in the qualitative theory of solutions of ordinary differential equations ... reduced to the one of (3) and (4) Then' are SOII1 P results on the stability of this class of differential equations (see [2, 7Ị) I I M ain R esults We assume in this section the following conditions:

Ngày tải lên: 14/12/2017, 19:52

... States This equation incorporates six key factors that influence soil erosion rates.Since 1990, the application of Geographic Information Systems (GIS) in assessing soil erosion in Vietnam has ... researches, with 8.250 experimental indice of 35 stations, Wishmeier (1985) found the product between kinetic energy of rain and maximum rainfall intensity in 30 minutes singned EI30 This value reflect ... ammount of soil loss and rain mode Wishmeier proposed equation to calculate R fsctor based on EI30 as follow: In which: R: Rainfall and runoff erosivity index I 30: Maximum rainfall in 30 minutes

Ngày tải lên: 23/06/2021, 16:50

... 557.9 hectares of vacant land (Forest Inventory and Planning Institute of VFU) The region experiences a rainy season that accounts for over 70% of total rainfall, leading to flooding in the headwater ... effect of rain and flow to on erosion Figure 4.2 R factor map in Lam Son commune Table 4.2 K index of some types of soil in Lam Son Commune Symbol K index Total area (km 2 ) The findings indicate ... researches, with 8.250 experimental indice of 35 stations, Wishmeier (1985) found the product between kinetic energy of rain and maximum rainfall intensity in 30 minutes singned EI 30 This value reflect

Ngày tải lên: 23/06/2021, 17:16

... simulated using the coupled perturbed density functional theory, showing an increasing dynamic β HRS value along with an increase in incident light energy Key words: Phthalocyanine, DFT, second-order ... moment 1 Introduction Nonlinear optical (NLO) materials have been intensively studied in recent decades because of their extensive applications in the fields of all-optical switching, optical information ... Nature of second-order nonlinear optical response in phthalocyanine derivatives: a density functional theory study Chiming WANG, Chao CHEN, Qingqi ZHANG, Dongdong QI∗, Jianzhuang JIANG Beijing Key

Ngày tải lên: 12/01/2022, 23:23

... decades These investigations were for non-Newtonian fluids of the differential type [6] In the case of fluids of differential type, the equations of motion are of order higher than that of the Navier–Stokes ... series in a very different manner By applying the MDTM the interval of con-vergence for the series solution is increased The MDTM is treated as an algorithm in a sequence of intervals for finding ... for systems of differential equations It is predicted that the MDTM can be applied to a wide range of engineering applications Keywords: Non-Newtonian Fluid, Stretching Surface, Shrinking Sheet,

Ngày tải lên: 19/11/2022, 11:46

... (Forest Inventory and Planning Institute of VFU) The region experiences a rainy season accounting for over 70% of total annual rainfall, often leading to flooding in the headwater catchment of the ... as engaging in cattle grazing and poultry farming Key weather data indicative of the regional climate are summarized in the accompanying table. Table1.1 Basis criteria datum of weather in the ... reflecting seasonal variations in moisture content.The wind regime in the study area is primarily characterized by two main wind directions: the Southeast wind, which predominates during the rainy

Ngày tải lên: 08/08/2023, 01:10

... Unbounded Solutions of Second-Order Multipoint Boundary Value Problem on the Half-Line 1 School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China 2 Department of Mathematics ... uniqueness of unbounded positive solution are obtained based upon the fixed point index theory and Banach contraction mapping principle Examples are also given to illustrate the main results 1 Introduction ... f : R× R × R → R is continuous, in whichR 0, ∞, R  −∞, ∞. The study of multipoint boundary value problemsBVPs for second-order differential equations was initiated by Bicadze and Samarsk˘ı

Ngày tải lên: 21/06/2014, 11:20

... existence and multiplicity of nodal solutions of the nonlinear second-order two-point boundary value problems, u00+ f (t, u) = 0, t ∈ (0, 1), u(0) = u(1) = 0 The proof of our main results is based upon ... and L´opez-G´omez [7], the proofs of these theorems contain gaps, the original statement of Theorem 1.40 of [4] is not correct, the original statement of Theorem 1.27 of [4] is stronger than what ... solutions of second-order two-point boundary value problemsDepartment of Mathematics, Northwest Normal University, Lanzhou 730070, P R China mary@nwnu.edu.cn yanglina7765309@163.com ∗ Corresponding

Ngày tải lên: 21/06/2014, 17:20

... 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

... 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 ... 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 equation ... 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

Ngày tải lên: 21/06/2014, 20:20

... 1. Hence, beginning with some k ,Equation 2.6 has exactly one positive root corresponding to the imaginary root of Equation 2.5. Now, find the asymptotic of the imaginary roots of Equation 2.5. ... numerator in the vicinity of zero is O(z ν+1 ), and the order of its denominator is O(z ν ), the integral along the left part of contour vanishes. Now, consider the integrals along the remaining three ... real roots. Proof. l is real since it is eigenvalue of self-adjoint operator associated with problem (2.1), (2.2). g k is real by our assumption (A*=A). Hence, the roots of (2.5) are square roots of real...

Ngày tải lên: 21/06/2014, 02:20

... data MIN_VAL: Min value of data TFmax: Max of transformation function TFmin: Min of transformation function OV: Original Value Application Application Training Training Training tunes a neural ... training, and testing. CONTENT CONTENT Introduction Introduction Steps in data forecasting modeling Steps in data forecasting modeling using neural network using neural network Determine ... employed in training the network. The test set, often includes 10% to 30% of training set, is used in testing the generalization. And the verification set is set balance between the needs of enough...

Ngày tải lên: 28/04/2014, 10:18