1,721,071 research outputs found
The algebraic structure of quaternionic analysis
No full textThe regularity of a quaternionic function is reinterpreted through a new canonical decomposition of the real differential, giving new insights into the algebraic properties of the regularity itself. The result comes from a somewhat unusual point of view on the automorphisms of the quaternionic field: a general notion of quaternionic linearity is associated to them, and some unnoticed metric properties of their inner representation are used to build up the theory
Fredholm's alternative for a class of almost periodic linear systems
No full textA Fredholm alternative is proposed for linear almost periodic equations which satisfy the Favard separation condition. The alternative is then tested in the special case, where all the solutions of the homogeneous part of the equation are bounded
A Stepanov version for Favard theory
No full textSome recent papers suggest that the classical Favard theory may be improved, by using the weak version of almost periodicity due to Stepanov: this note is to say that the improvement is just apparent
The Favard Separation Condition for Almost Periodic Linear Systems
No full textFor linear systems which depend almost periodically on time, the Favard separation condition is shown to be equivalent to the following dimensional fact: all the systems in the hull have the same number of independent bounded solutions
Module containment property for linear equations
No full textAbstractA general module containment property is proved for almost periodic linear systems of differential equations, in both finite and infinite dimensions
On the count and the classification of periodic solutions to forced pendulum-type equations
No full text
Large minimal period orbits of periodic autonomous systems
No full textWe prove the existence of periodic orbits with minimal period greater than any prescribed number for a natural Lagrangian autonomous system in several variables that is analytic and periodic in each variable and whose potential is nonconstant
Almost periodic equations and conditions of Ambrosetti-Prodi type
No full textWe discuss the exact number of almost periodic solutions of certain ordinary differential equations of the second order. The class of equations under consideration is inspired by a well-known result in the area of elliptic boundary value problems
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