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On a new class of abstract integral equations and applications
(ELSEVIER SCIENCE INCNEW YORK, 2012)
In this paper we introduce a new class of abstract integral equations which enables us to study in a unified manner several different types of differential equations. (C) 2012 Elsevier Inc. All rights reserved.
Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
(2021-01-01)
Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class of ...
Evaluating residues and integrals through negative dimensional integration method (NDIM)
(2006-10-01)
The standard way of evaluating residues and some real integrals through the residue theorem (Cauchy's theorem) is well-known and widely applied in many branches of Physics. Herein we present an alternative technique based ...
Evaluating residues and integrals through negative dimensional integration method (NDIM)
(2006-10-01)
The standard way of evaluating residues and some real integrals through the residue theorem (Cauchy's theorem) is well-known and widely applied in many branches of Physics. Herein we present an alternative technique based ...
A family of singular ordinary differential equations of the third order with an integral boundary condition
(Springer, 2018-12)
We establish in this paper the equivalence between a Volterra integral equation of the second kind and a singular ordinary differential equation of the third order with two initial conditions and an integral boundary ...
EXPLICIT VARIATIONAL FORMS FOR THE INVERSES OF INTEGRAL LOGARITHMIC OPERATORS OVER AN INTERVAL
(SIAM PUBLICATIONS, 2012)
We introduce explicit and exact variational formulations for the weakly singular and hypersingular operators over an open interval as well as for their corresponding inverses. Contrary to the case of a closed curve, these ...
On the Norm with Respect to Vector Measures of the Solution of an Infinite System of Ordinary Differential Equations
In the present paper we give some necessary conditions that satisfy the solutions of an infinite system of ordinary differential equations. We investigate the behavior of the solutions of a general system of equations, ...