first order differential equations in real life

... reproduction in any medium, provided the original work is properly cited. Boundary Value Problems manuscript No. (will be inserted by the editor) Minimal and maximal solutions to first -order differential equations ... solution of (1) in Y if x ∗ ≤ x (respectively, x ∗ ≥ x) for any other solution x ∈ Y . Notice that the least solution in a subset Y is a minimal solution in Y , but the converse is false in general, ... (1) in [ α, β ] has maximal and minimal elements. The set S = {x ∈ C(I) : x is a solution of (1) , x ∈ [α, β]} is nonempty and compact in C(I), beacuse it coincides with the set of fixed points...

Ngày tải lên: 20/06/2014, 20:20

... Liapunov-type inequality for certain higher -order differential equations. Appl. Math. Comput. 134(2–3), 307–317 (2003) [17] Cakmak, D: Lyapunov-type integral inequalities for certain higher order differential equations. ... 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 ... a)   b  a |x  (s)| 2 ds   1/2 , ∀ t ∈ [a, b]. (2.1) In the meantime, in order to obtain Lemma 2.3 which also plays an important role in this article, we will apply the following inequality. See Lemma 2.2. Lemma...

Ngày tải lên: 20/06/2014, 21:20

... inte- ger -order ordinary differential equations. Toidentifyafew,wereferthereaderto [2-13] and the references therein. Fractional differential equations arise in many engineering and scientific disciplines as ... Three-point boundary value problem, Fractional differ- ential equations, Guo-Krasnoselskii fixed point theorem, Cone 1 Introduction The study of three-point BVPs for nonlinear integer -order ordinary ... accurate than integer- order models, i.e., there are more degrees of freedom in the fractional -order models. In consequence, the subject of fractional differential equations is gaining much impor- tance...

Ngày tải lên: 21/06/2014, 03:20

... Our main result is established by using fractional powers of linear operators and Banach contraction principle. The obtained result can be seen as a contribution to thi s emer- ging field since ... stochastic differential equations in a real separable Hilbert space. We study also some properties of square-mean almost automorphic functions including a compostion theorem. To establish our main results, ... solutions on different kinds of deterministic differential equations have been considerably investigated in lots of publications [5-15] because of its signifi- cance and applications in physics, mechanics,...

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... results in the discrete and the continuous calculus; for instance, some results obtained separately for delay difference equations and delay-differential equations can be incorporated in the general ... ∞ T , Hindawi Publishing Corporation Advances in Difference Equations Volume 2010, Article ID 873459, 22 pages doi:10.1155/2010/873459 Research Article Nonoscillation of First- Order Dynamic Equations with ... imply that e −Λ t, s is nondecreasing in s, hence e −Λ  1/e −Λ t, s is nonincreasing in s see 4, Theorem 2.36.From4.15 and Advances in Difference Equations 3 Theorem A is the generalization...

Ngày tải lên: 21/06/2014, 11:20

... Applications Results derived in Theorems 4.1 and 4.2 constitute a useful tool when investigating the solvability of nonlinear singular equations subject to different types of boundary conditions. In this section, ... analysis of more involved nonlinearities, where typically, f has singular points also in u and u  . Many applications, compare 2–12, showing these structural difficulties are our main motivation ... compact subinterval I ⊂ J and having absolutely continuous first derivatives on each compact subinterval I ⊂ J, respectively. As already said in the previous section, we investigate differential equations...

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... methods involve new differential inequalities and the classical fixed-point theory. This paper mainly considers the existence of solutions for the following first- order nonlinear integro -differential ... developments involving existence of solutions to BVPs for integro -differential equations and impulsive integro -differential equations we can refer to [3-17]. So far the m ain method appeared in the ... nonlinear first order ordinary differential equations. Math Inequal Appl. 6, 477–485 (2003) 23. Luo, ZG, Shen, JH, Nieto, JJ: Antiperiodic boundary value problem for first -order impulsive ordinary...

Ngày tải lên: 21/06/2014, 02:20

... concerns the possibility of allowing jumps in their graphs. Since the task of finding a pair of lower and upper solutions is by no means easy in general, and bearing in mind that constant lower and ... contradiction. Hindawi Publishing Corporation Boundary Value Problems Volume 2009, Article ID 507671, 25 pages doi:10.1155/2009/507671 Research Article First- Order Singular and Discontinuous Differential Equations Daniel ... and since these can be transformed into continuous ones which provide better information we will only consider from now on continuous lower and upper solutions as defined in Definition 2.1. 5. Singular...

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Ngày tải lên: 22/06/2014, 03:20

... supermartingale is trending systematically downward or has no trend. We call a supermartingale a strict supermartingale (strict sub- martingale) if the inequality in (1.2.6) is always a strict inequality. As ... Milstein (1974). By adding the double Wiener integrals to the Euler scheme one obtains the Milstein scheme, thus enhancing the order of strong convergence from γ =0.5toγ =1.0. Nonethe- less, the order ... with stationary independent increments. These basic processes have mathemati- cal properties that make them suitable as fundamental building blocks in stochastic modeling and, thus, in financial modeling....

Ngày tải lên: 19/02/2014, 22:20

... physical activities (standing, sitting, walking, lying, reclining, step- ping, etc), walking speed, and energy expenditure pro- duced during activities (EE - measured in kcal/min or kJ/ min or Watts). The ... validity of gait data. In the present study, even a trend in reduced time spent in walking and standing was present as well as an increasing in time spent sitting and a reduction in number of steps walked, ... in obese subjects, and probably this greater energetic demand makes the obese subject to leading a less active life reinforcing a vicious circle. Also this finding is in agreement with data in...

Ngày tải lên: 19/06/2014, 08:20