122 research outputs found
Asymptotic solutions of forced nonlinear second order differential equations and their extensions
Using a modified version of Schauder's fixed point theorem, measures of
non-compactness and classical techniques, we provide new general results on the
asymptotic behavior and the non-oscillation of second order scalar nonlinear
differential equations on a half-axis. In addition, we extend the methods and
present new similar results for integral equations and Volterra-Stieltjes
integral equations, a framework whose benefits include the unification of
second order difference and differential equations. In so doing, we enlarge the
class of nonlinearities and in some cases remove the distinction between
superlinear, sublinear, and linear differential equations that is normally
found in the literature. An update of papers, past and present, in the theory
of Volterra-Stieltjes integral equations is also presented
A new Pachpatte type dynamic inequality on time scales
In this paper, using the comparison theorem, we investigate a new Pachpatte type dynamic inequality on time scales, which provides explicit bounds on unknown functions. Our result unifies and extends a continuous inequality and its corresponding discrete analogues
New Challenges Arising in Engineering Problems with Fractional and Integer Order
Mathematical models have been frequently studied in recent decades, in order to obtain the deeper properties of real-world problems. In particular, if these problems, such as finance, soliton theory and health problems, as well as problems arising in applied science and so on, affect humans from all over the world, studying such problems is inevitable. In this sense, the first step in understanding such problems is the mathematical forms. This comes from modeling events observed in various fields of science, such as physics, chemistry, mechanics, electricity, biology, economy, mathematical applications, and control theory. Moreover, research done involving fractional ordinary or partial differential equations and other relevant topics relating to integer order have attracted the attention of experts from all over the world. Various methods have been presented and developed to solve such models numerically and analytically. Extracted results are generally in the form of numerical solutions, analytical solutions, approximate solutions and periodic properties. With the help of newly developed computational systems, experts have investigated and modeled such problems. Moreover, their graphical simulations have also been presented in the literature. Their graphical simulations, such as 2D, 3D and contour figures, have also been investigated to obtain more and deeper properties of the real world problem
An Exactly Solvable Phase-Field Theory of Dislocation Dynamics, Strain Hardening and Hysteresis in Ductile Single Crystals
An exactly solvable phase-field theory of dislocation dynamics, strain
hardening and hysteresis in ductile single crystals is developed. The theory
accounts for: an arbitrary number and arrangement of dislocation lines over a
slip plane; the long-range elastic interactions between dislocation lines; the
core structure of the dislocations resulting from a piecewise quadratic Peierls
potential; the interaction between the dislocations and an applied resolved
shear stress field; and the irreversible interactions with short-range
obstacles and lattice friction, resulting in hardening, path dependency and
hysteresis. A chief advantage of the present theory is that it is analytically
tractable, in the sense that the complexity of the calculations may be reduced,
with the aid of closed form analytical solutions, to the determination of the
value of the phase field at point-obstacle sites. In particular, no numerical
grid is required in calculations. The phase-field representation enables
complex geometrical and topological transitions in the dislocation ensemble,
including dislocation loop nucleation, bow-out, pinching, and the formation of
Orowan loops. The theory also permits the consideration of obstacles of varying
strengths and dislocation line-energy anisotropy. The theory predicts a range
of behaviors which are in qualitative agreement with observation, including:
hardening and dislocation multiplication in single slip under monotonic
loading; the Bauschinger effect under reverse loading; the fading memory
effect, whereby reverse yielding gradually eliminates the influence of previous
loading; the evolution of the dislocation density under cycling loading,
leading to characteristic `butterfly' curves; and others
Some New Delay Integral Inequalities in Two Independent Variables on Time Scales
Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of boundedness of solutions of delay dynamic equations on time scales. Some of the established results are 2D extensions of several known results in the literature, while some results unify existing continuous and discrete analysis
Abstract book
Welcome at the International Conference on Differential and Difference Equations
& Applications 2015.
The main aim of this conference is to promote, encourage, cooperate, and bring
together researchers in the fields of differential and difference equations. All areas
of differential & difference equations will be represented with special emphasis on
applications. It will be mathematically enriching and socially exciting event.
List of registered participants consists of 169 persons from 45 countries.
The five-day scientific program runs from May 18 (Monday) till May 22, 2015
(Friday). It consists of invited lectures (plenary lectures and invited lectures in
sections) and contributed talks in the following areas:
Ordinary differential equations,
Partial differential equations,
Numerical methods and applications, other topics
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