Resumen de Resolubilidade de problemas lineares de cauchy em espaços de fréchet e um modelo de kaldor com retardo

Alex Pereira da Silva

• The long-run aim of this thesis is to solve delay differential equations with infinite delay of the type d/dt u (t)=Au(t)+∫_(-∞)^t▒〖u(s)k (t-s)ds+ "f" ("t,u(t)" ) 〗 on Fréchet spaces under an extended theory of groups of linear operators; where A is a linear operator, k(s) ⩾ 0 satisfies ∫_0^∞▒〖k(s)ds=1〗 and f is a nonlinear map.

  In order to pursue such a goal we study a discrete delay model which explains the natural economic fluctuations considering how economic stability is affected by the role of the fiscal and monetary policies and a possible government inefficiency concerning its fiscal policy decision-making. On the other hand, we start to develop such an extended theory by considering linear Cauchy problems associated to a continuous linear operator on Fréchet spaces, for which we establish necessary and sufficient conditions for generation of a uniformly continuous group which provides the unique solution. Further consequences arises by considering pseudodifferential operators with constant coefficients defined on a particular Fréchet space of distributions, namely 〖FL〗_loc^2 , and special attention is given to the distributional solution of the heat equation on 〖FL〗_loc^2 loc for all time, which extends the standard solution on Hilbert spaces for positive time.