On Frechet differentiability of some nonlinear operators occurring in inverse problems: an implicit function theorem approach

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Mixed constraints in optimal control: an implicit function theorem approach

According to a widely quoted paper by Gilbert and Bernstein (1983), ‘mathematical rigorous treatments of second order necessary conditions for problems in optimal control seem to be limited’. In that paper, two different sets of second-order conditions are obtained by applying necessary conditions for an abstract optimization problem developed by the second author (Bernstein, 1984). These condi...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

On the Inverse Function Theorem

An inverse function theorem in Fréchet spaces

I present an inverse function theorem for differentiable maps between Fréchet spaces which contains the classical theorem of Nash and Moser as a particular case. In contrast to the latter, the proof does not rely on the Newton iteration procedure, but on Lebesgue’s dominated convergence theorem and Ekeland’s variational principle. As a consequence, the assumptions are substantially weakened: th...