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A new application of the homotopy analysis method in solving the fractional Volterra's population system

Mehdi Ghasemi, Mojtaba Fardi, Reza Khoshsiar Ghaziani (2014)

Applications of Mathematics

This paper considers a Volterra's population system of fractional order and describes a bi-parametric homotopy analysis method for solving this system. The homotopy method offers a possibility to increase the convergence region of the series solution. Two examples are presented to illustrate the convergence and accuracy of the method to the solution. Further, we define the averaged residual error to show that the obtained results have reasonable accuracy.

A new method to obtain decay rate estimates for dissipative systems

Patrick Martinez (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the wave equation damped with a boundary nonlinear velocity feedback p(u'). Under some geometrical conditions, we prove that the energy of the system decays to zero with an explicit decay rate estimate even if the function ρ has not a polynomial behavior in zero. This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction...

A nonexistence result for the Kurzweil integral

Pavel Krejčí, Jaroslav Kurzweil (2002)

Mathematica Bohemica

It is shown that there exist a continuous function f and a regulated function g defined on the interval [ 0 , 1 ] such that g vanishes everywhere except for a countable set, and the K * -integral of f with respect to g does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.

A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces

Jacek Jachymski (2005)

Studia Mathematica

We establish a Banach-Steinhaus type theorem for nonlinear functionals of several variables. As an application, we obtain extensions of the recent results of Balcerzak and Wachowicz on some meager subsets of L¹(μ) × L¹(μ) and c₀ × c₀. As another consequence, we get a Banach-Mazurkiewicz type theorem on some residual subset of C[0,1] involving Kharazishvili's notion of Φ-derivative.

Currently displaying 81 – 100 of 305