A generalized Picard-Lindelöf theorem

On a Theorem of Picard

We extend Picard's theorem on the existence of elliptic solutions of the second kind of linear homogeneous n th-order scalar ordinary diierential equations with coeecients being elliptic functions (associated with a common period lattice) to linear homogeneous rst-order n n systems. In particular, the qualitative structure of the general solution in terms of elliptic and exponential functions, ...

A Picard type theorem for holomorphic curves∗

Let P be complex projective space of dimension m, π : Cm+1\{0} → P the standard projection and M ⊂ P a closed subset (with respect to the usual topology of a real manifold of dimension 2m). A hypersurface in P is the projection of the set of zeros of a non-constant homogeneous form in m+ 1 variables. Let n be a positive integer. Consider a set of hypersurfaces {Hj} j=1 with the property M ∩ ⋂...

Picard ' S Theorem by Douglas Bridges

This paper deals with the numerical content of Picard's Thsorem. Two classically equivalent versions of this theorem are proved which are distinct from a computational point of view. The proofs are elementary, and constructive in the sense of Bishop. A Brouwerian counterexample is given to the original version of the theorem.

A Fixed Point Theorem in Generalized D-metric Spaces

Generalized Unitaries and the Picard Group

After discussing some basic facts about generalized module maps, we use the representation theory of the algebra Ba(E) of adjointable operators on a Hilbert B–module E to show that the quotient of the group of generalized unitaries on E and its normal subgroup of unitaries on E is a subgroup of the group of automorphisms of the range ideal BE of E in B. We determine the kernel of the canonical ...