Set Differential Equations in Fréchet Spaces
نویسندگان
چکیده
منابع مشابه
Set Differential Equations in Fréchet Spaces
It is known that a Fréchet space F can be realized as a projective limit of a sequence of Banach spaces Ei. The space Kc(F) of all compact, convex subsets of a Fréchet space, F, is realized as a projective limit of the semilinear metric spacesKc(E). Using the notion of Hukuhara derivative for maps with values inKc(F), we prove the local and global existence theorems for an initial value problem...
متن کاملDifferential Equations in Fréchet Differentials Occurring in Integral Equations.
1 Kasner, "Algebraic Potential Curves," BuO. Am. Math. Soc., 1901. 2 Kasner, "Conformal Geometry," Proc. Fifth Internat. Cong. of Math., 2, 81 (1912). 3 Kasner, "Geometry of Conformal Symmetry (Schwarzian Reflection)," Ann. Math., 38, 873 (1937). 4 Comenetz, "Conformal Geometry on a Surface," Ibid., 39, 863 (1938). I wish to thank J. De Cicco, Aida Kailish, F. Supnik and C. Vlucay for assistanc...
متن کاملFUZZY FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN PARTIALLY ORDERED METRIC SPACES
In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.
متن کاملDifferential Equations in Metric Spaces
We give a meaning to derivative of a function u : → X, where X is a complete metric space. This enables us to investigate differential equations in a metric space. One can prove in particular Gronwall’s Lemma, Peano and Picard Existence Theorems, Lyapunov Theorem or Nagumo Theorem in metric spaces. The main idea is to define the tangent space TxX of x ∈ X. Let u, v : [0, 1) → X, u(0) = v(0) be ...
متن کاملMetric Spaces and Differential Equations
The concepts of metric spaces (complete and incomplete) and associated topics are illustrated and used to prove existence and uniqueness theorems in the theory of differential equations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Analysis
سال: 2008
ISSN: 1425-6908,1869-6082
DOI: 10.1515/jaa.2008.103