the notation of higher order differential equations

... (KVL): The algebraic sum of allthe instantaneous voltage drops around any closed loop is zero, or thevoltage impressed on a closed loop is equal to the sum of the voltagedrops in the rest of the ... into mathematical terms: (A) To choose the (physical, natural, ) laws governing the problem. (B) To choose mathematical variables. (C) To establish the (differential) equations. Analysis of the ... natural, ) laws governing the problem. (B) To choose mathematical variables. (C) To establish the (differential) equations. (A) To solve equations (B) To find the properties of solutions (C) If it

Ngày tải lên: 23/04/2020, 08:00

... function of a related linear operator in the space of the antiperiodic functions 1 Introduction The theory of dynamic equations has been introduced by Stefan Hilger in his Ph.D thesis [12] This new theory ... is rd-continuous in I. Proof As we have seen in the proof ofTheorem 2.2, we know that Green’s function asso-ciated to the operatorT −1inW nis given as the 1× n term of the matrix function F(t,s) ... Using the results proved in Sections2and3, we will obtain in Sections4and5the expression of Green’s function and a sufficient condition for the existence and uniqueness of solutions of the dynamic equations

Ngày tải lên: 23/06/2014, 00:20

... 23, 38] and the references therein formore details) The applications of the method of sums of commuting operatorsinto the study of almost periodic solutions of functional di¤erential equationscan ... usual, sðTÞ; rðTÞ; Rðl; TÞ are the notations of the spectrum, resolvent set and resolvent of the operator T. The notations BUC ðR; XÞ; APðXÞ will stand for the space of all X-valued bounded uniformly ... semigroup, all conclusions of Theorem 3.4 hold true from the composition of the variation of constants formula de-Theorem 3.7 Let A be the generator of a compact semigroup Then, Eq (1) has a 1-periodic

Ngày tải lên: 16/12/2017, 01:01

... results on the existence of periodic solutions we refer the reader to [19, 4, 16, 25, 22] When f is periodic the method of study in these works is to prove the existence of fixed points of the period ... neighborhood of iξ Proof For the proof we refer the reader to [24, Proposition 0.5, p.22] We collect some main properties of the spectrum of a function, which we will need in the sequel, for the reader’s ... Proof For the proof (of more general results) we refer the reader to [15], [14, Chap 4] Next, we gather some further properties of the almost periodic spectrum SpAP(f ) by quoting here another

Ngày tải lên: 16/12/2017, 16:50

... examines the significance of the risk factors in the CAPM with higher order co-moments using a two-pass methodological technique of Fama and Macbeth Stock prices of 53 companies out of the 207 ... Nigeria with the aim of testing if the model will improve the descriptive power of the CAPM which was hitherto tested using Nigerian monthly stock prices by (Arewa, 2008) The rests of the paper ... sample of weekly returns of the most liquid Russian stocks over the financially stable period of 2004-2007 and over the crisis period of 2008-2009 to test the CAPM with higher moments They confirm

Ngày tải lên: 01/02/2020, 22:54

... emphasized that in the monotone method the assumption of the presence of lower and upper solutions is always needed and the finding of them is not easy The system of fourth-order differential equations ... or unknown, to demonstrate the applicability of the obtained theoretical results and the efficiency of the iterative method 4 The major contribution of the thesis The thesis proposes a method for ... solving the boundary value problems for differential equations Among the differential equations, the nonlinear fourth-order differential equation has been of great interest recently as it is the mathematical

Ngày tải lên: 01/04/2021, 19:17

... rain falls there are large deserts without many rivers and lakes As the climate and vegetation® of one place are not the same as those of another, the habits and activities of the people of different ... fertilize their lands and to provide a means of communication for the goods that they transport from place to place Early civilization’ began on the banks` of the great rivers of the world, such as the ... different parts of the world They were all very active, though they had been confined' to their cages for a long time Then, we went to the places where the tigers and the lions were kept These animals

Ngày tải lên: 25/10/2013, 06:20

... about the integers There are higher-order logics that have been provided which con- tain the formulas of second-order logic b u t which do not assume the same notion of models (i.e the integers) These ... theorem proving in higher-order logic t h a n in first-order logic as claimed in the last point, the nature of proofs in higher-order logic is far from mysterious For example, higher-order resolution ... below a brief exposition of the higher-order features of this language that we shall use in the examples in the later sections A fuller descrip- tion of the language and of the logical considerations

Ngày tải lên: 21/02/2014, 20:20

... discussion of the role of higher education in economic development and specific actions taken by the institutions of the Higher Education Alliance for the Rock River Region (HEARRR): Northern Illinois ... help achieve these goals (Sampson, 2003; 2004) The focus of this report is the role of higher education in the economic development of Illinois’ Rock River Region A brief summary of economic development ... work together to attract students into critical programs • The members of the Alliance match instructional programs to the economic growth needs of the region In the past three years, they have

Ngày tải lên: 17/03/2014, 07:20

... a means ofsaving money A Strategy Va c u u m ? Yet, given the harsh reality of ‘the politics of HE’ and the voting power ofthe better-off, the White Paper proposals may yet run into the sand,leaving ... majorpart of the cost of higher education for the better-off With reference to the US, Johnstone noted that here the student’s share of the cost of HE was ‘already the heaviest of any nation’, while ... debate of 27 January 2004 on the second reading ofthe Higher Education Bill, where the Government scraped by with ahumiliating margin of just five votes, the furore over the future andfunding of

Ngày tải lên: 23/03/2014, 20:20

... features None of the other known C splice variants are encoded with the same N-terminus as Ca1 and Cb1 and it is not expected that they undergo the same type of modifications Thus, they may harbor ... that the b-gene of the catalytic (C) subunit of protein kinase A encodes a number of splice variants These splice variants are equipped with a variable N-terminal end encoded by alternative use of ... N-terminus of Ca1 and Cb1 are more homologous to each other than to any of their splice variants In the case of Ca1, three sites may undergo co- and post-translational modifications At the very

Ngày tải lên: 30/03/2014, 04:20

... solutions The first result ensures theexistence of maximal and minimal solutions, and the second one establishesthe existence of the greatest and the least solutions in a particular case Theconcepts of ... Therefore, if f is nondecreasing with respect to its third variable, then Definition 1 and the usual definition of lower and upper solutions are the same (we will use this fact in the proof of ... solution is neither the least nor the greatest solution of (10) in [α, β] Now let ˆ x ∈ [α, β] be an arbitrary solution of problem (10) and let us prove that ˆx is neither the least nor the greatest

Ngày tải lên: 20/06/2014, 20:20

... because of both practical and theoretical aspects There have been many papers investigating the solutions of three-point BVPs, see 2 5, 10, 12 and references therein Recently, the existence of solutions ... and the existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory Motivated by the above works, we consider the singular third-order ... known results 1 Introduction Third-order differential equations arise in a variety of different areas of applied mathematics and physics, such as the deflection of a curved beam having a constant

Ngày tải lên: 21/06/2014, 05:20

... regularly varying sequences, useful to the development of the theory in the subsequent sections, are listed in the following proposition The proofs of the statements can be found in 1 4,5 Proposition ... examined by means of the contraction mapping theorem in the Banach space of sequences converging towards zero The following properties of h will play a crucial role in the proof The first two are ... positive, if c2  0, then necessarily c1 > 0 and z ∈ NRV1 If c2/ 0, then we getc2 > 0 because of the positivity of z kfork large and the strict inequality between the indices of regular variation1<

Ngày tải lên: 21/06/2014, 11:20

... solution of 2.1, then x can be written in the following form: Trang 5Proof As the uniqueness for the solution of2.1 was proven in 5, it suffices to show thatfor each t ∈ t0,∞T The proof is therefore ... delay dynamicequations, and from now on, we will without further more mentioning suppose that the timescaleT is unbounded from above because of the definition of oscillation The object of thepresent ... R t1,∞T,R AndTheorem 3.1 reduces is a positive solution of 3.2, and −x is a negative solution to 3.3. The following three examples are special cases of the above result, and the first two ofthem

Ngày tải lên: 21/06/2014, 11:20

... existence theorem for single and multiple positive periodic solutions of (1.3) Our aim of this article is to study the existence of periodic solutions for the higherorder difference equations ... the existence of periodic solutions for the higherorder difference equation x(n + k) = g(x(n)) − f (n, x(n − τ (n)) We show the existence of periodic solutions by using Schauder’s fixed point theorem, ... fixed point theorem 1 Introduction and main results Let R denote the set of the real numbers, Z the integers and N the positive integers In this article, we investigate the existence of periodic...

Ngày tải lên: 18/06/2014, 22:20

... interval symmetrizes about the origin Then, similar to the proof of (2.9), we can verify the condition f (α) = f (β), and the other conditions in Lemma 2.2 are satisfied all the way Hence, it also ... [α, β], too Then, by a similar method to the proof of (2.3) together with Lemma 2.2, we can obtain (2.4) immediately For the other ordinary cases, i.e., a = 0, we only need to move the interval ... for a class of even -order differential equations Qi-Ming Zhang∗1 and Xiaofei He2 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R China College of Mathematics and...

Ngày tải lên: 20/06/2014, 21:20

... and they give rise to many applications see Not only the new theory of the so-called “dynamic equations unifies the theories of differential equations and difference equations but also extends these ... G ut p τ Δτ ≤ G u T 2.53 P T The rest of the proof is similar to that of Theorem 2.8, and the details are omitted The proof is completed Theorem 2.10 Assume that the function f t, u0 , , un−1 ... discrete analysis The cases when a time scale is equal to the real numbers or to the integers represent the classical theories of differential and of difference equations Many other interesting...

Ngày tải lên: 21/06/2014, 05:20

... for the existence of positive solutions The purpose of this paper is to investigate further the singular BVP for delay higherorder dynamic equation 1.1 By the use of the fixed point theorem of ... on the existence of positive solutions to the BVP 1.1 are established The paper is organized as follows In Section 2, we give some lemmas, which will be required in the proof of our main theorem ... Tk T − {t2 } ; otherwise, set Tk T Tk T By an interval a, b we always mean the intersection of the real interval a, b with the given time scale, that is, a, b ∩ T Other types of intervals are...

Ngày tải lên: 21/06/2014, 20:20

... (3:8) then (1.1) is oscillatory or tends to zero as t ® ∞ Proof The proof of the corollary is similar to the proof of Corollary 3.3 and so it is omitted From the above results on the oscillation of ... (2:13) then every solution of (1.1) is oscillatory or tends to zero as t ® ∞ Proof The proof of the corollary is similar to the proof of Corollary 2.8 and so it is omitted Example 2.11 Consider the ... Oscillation of solutions of non-linear neutral delay differential equations of higher order for p(t) = ± Arch Math 40, 359–366 (2004) Tang, S, Li, T, Thandapani, E: Oscillation of higher- order half-linear...

Ngày tải lên: 20/06/2014, 22:20