Regularização de um problema com singularidade não somável

Abstract

The mathematical description of many real processes leads to boundary problems for equations like rc(í) = /(í,x(h(t))}, t and [a, ò], rc(£) = y(Ç), £ and [a, 6]. (1) Equation (1) is a current example of a functional differential equation. Functional differential equations contain special classes of equations, such as ordinary differential equations and integral-differential equations. The investigation of issues specific to special classes of functional differential equations is portrayed in many articles and monographs. In Hale's monograph [7] an attempt is made to systematize a wide range of results from the Theory of Differential Functional Equations. However, the construction of the foundations of the general theory of functional differential equations was made possible thanks to the conception proposed by Professor Doctor NV Azbelev (see, for example, [5]). Within the scope of this conception, the functional differential equation was understood to be an equation of form x = J-x, with operator T7 defined in a certain subset of the space of absolutely continuous functions W}[a, 6]. In the Theory of Functional Differential Equations, an important role plays in the fact that the space W}[a, ò] is isomorphic to the direct product of the space Li[a,6] of summable functions and the finite-dimensional space R1. For example, this isomorphism can be defined according to the correspondence 9 x —> {£, x(a)} € Li [a, 6] x R1