On a second order differential equation with piecewise constant mixed arguments

Author: H. Bereketoglu / G. Seyhan / F. Karakoc

Abstract: We prove the existence and
uniqueness of solutions of a class of second order differential equations
with piecewise constant mixed arguments and we show that the
zero solution of Eq. (1.1) is a global attractor. Also, we study
some properties of solutions of Eq. (1.1) such as oscillation, nonoscillation, and periodicity. PDF |

No. of downloads: 208

Stability of Picard iteration for contractive mappings satisfying an implicit relation

Author: Vasile Berinde

Abstract: We obtain new and very general stability results for Picard iteration associated to self operators satisfying an implicit relation. Our stability results unify, extend, generalize, enrich and complement a multitude of related stability results from recent literature. PDF |

No. of downloads: 204

Generalized Weyl's theorems for polaroid operators

Author: C. Carpintero / D. Munoz / E. Rosas / O. Garcia / J. Sanabria

Abstract: In this paper we establish necessary and sufficient conditions on bounded linear operators for which generalized Weyl's theorem, or generalized $a$-Weyl theorem, holds. We also consider generalized Weyl's theorems in the framework of polaroid operators and obtain improvements of some results recently established in [20] and [29].
PDF |

No. of downloads: 207

On controllability for a class of second-order differential inclusions

Author: Aurelian Cernea

Abstract: By using a suitable fixed point theorem a sufficient condition for
controllability is obtained for a Sturm-Liouville type
differential inclusion in the case when the right hand side has
convex values. PDF |

No. of downloads: 159

Positive periodic solutions for systems of second order differential equations

Author: Vasile Dincuță-Tănase

Abstract: In this paper we seek for positive periodic solutions for a system of second
order differential equations using a vector version of Krasnoselskii's Fixed
Point Theorem in Cones. This makes possible that the nonlinear term of the
system have different behaviors both in components and variables. PDF |

No. of downloads: 141

Analytical investigation of beam deformation equation using perturbation, homotopy perturbation, variational iteration and optimal homotopy asymptotic methods

Author: F. Farrokhzad / P. Mowlaee / A. Barari / A. J. Choobbasti / H. D. Kaliji

Abstract: The beam deformation equation has very wide applications in
structural engineering. As a differential equation, it has its own
problem concerning existence, uniqueness and methods of solutions.
Often, original forms of governing differential equations used in
engineering problems are simplified, and this process produces noise
in the obtained answers.
This paper deals with solution of second order of
differential equation governing beam deformation using four
analytical approximate methods, namely the Homotopy Perturbation
Method (HPM), Variational Iteration Method (VIM) and Optimal
Homotopy Asymptotic Method (OHAM). The comparisons of the results
reveal that these methods are very effective, convenient and quite
accurate to systems of non-linear differential equation. PDF |

No. of downloads: 158

Some applications of CHEVIE to the theory of algebraic groups

Author: Meinolf Geck

Abstract: The computer algebra system CHEVIE is designed to facilitate computations
with various combinatorial structures arising in Lie theory, like finite
Coxeter groups and Hecke algebras. We discuss some recent examples where
CHEVIE has been helpful in the theory of algebraic groups, in
questions related to unipotent classes, the Springer correspondence and
Lusztig families. PDF |

Boundary value problems for nonlinear systems with generalized second-order differences

Author: Rodica Luca

Abstract: In a real Hilbert space, we investigate the existence and uniqueness of the solutions for two classes of infinite nonlinear systems with generalized second-order differences, one of them subject to a boundary condition. Some applications to nonlinear differential systems with monotone operators are also presented. PDF |

No. of downloads: 134

Sufficient conditions for the existence of some nonoscillatory solutions of third-order
nonlinear differential equations

Author: Ivan Mojsej / Alena Tartalova

Abstract: The aim of this paper is to study the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the sufficient conditions ensuring the existence of some nonoscillatory solutions with a specified asymptotic property as $t$ tends to infinity. The basic tool used in proving our results is the classical Banach contraction mapping principle. PDF |

No. of downloads: 154

On a regularization technique for Kovarik-like approximate orthogonalization algorithms

Author: Aurelian Nicola / Constantin Popa / Ulrich Rude

Abstract: In this paper we consider four versions of Kovarik's iterative orthogonalization algorithm, for approximating the
minimal norm solution of symmetric least squares problems. Although the theoretical convergence rate of these
algorithms is at least linear, in practical applications we observed that a too big number of iterations can
dramatically deteriorate the already obtained approximation. In this respect we analyse the above mentioned
Kovarik-like methods according to the modifications they make on the ``machine zero'' eigenvalues of the problem's
(symmetric) matrix. We establish a theoretical almost optimal formula for the number of iterations necessary to obtain
an enough accurate approximation, as well as to avoid the above mentioned troubles. Experiments on collocation
discretization of a Fredholm first kind integral equation illustrate the efficiency of our considerations. PDF |

No. of downloads: 202

n-th relative nilpotency degree and relative n-isoclinism classes

Author: Rashid Rezaei / Francesco G. Russo

Abstract: P. Hall introduced the notion of isoclinism between two groups more
than 60 years ago. Successively, many authors have extended such a
notion in different contexts. The present paper deals with the
notion of relative n-isoclinism, given by N. S. Hekster in 1986,
and with the notion of n-th relative nilpotency degree, recently
introduced in literature. PDF |

No. of downloads: 150

Continuous dependence on a
parameter of the countable fractal interpolation function

Author: Nicolae-Adrian Secelean

Abstract: In this paper we will show that, if a countable interpolation data
depends continuously on a parameter and some proper continuity
conditions are fulfilled, then its associated attractor and the
corresponding countable fractal interpolation function depends also
continuously on the respective parameter. An example in R^2 is
given. PDF |

No. of downloads: 153

On approximating curves associated with nonexpansive mappings