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A novel approach to a coordinate-free analysis of the multiplier question in the inverseproblem of the calculus of variations, initiated in a previous publication, is completed in thefollowing sense: under quite general circumstances, the complete set of passivity or integrabilityconditions is...
We study the existence and uniqueness of solutions to the system of three-dimensionalNavier-Stokes equations and the continuity equation for incompressible fluid with mixedboundary conditions. It is known that if the Dirichlet boundary conditions are prescribed on thewhole boundary and the total...
Given a fixed point free antianalytic involution k of a domain G in thecomplex plane, bounded by a finite number of analytic curves, k-invariant Green’sfunctions are defined on G. The Lindelöf’s principle is extended to k-invariantGreen’s functions. When G is the annulus, k-invariant Green’s...
A large variety of Lp(p 0) form very general Opial type inequalities arepresented engaging different order generalized fractional derivatives of a function. These arebased on a generalization of Taylor’s formula for generalized fractional derivatives. In the finalresults of this work, a...
Two continuation methods are described in this paper. The first is based on essential mapswhereas the second is based on 0-epi maps.
The notion of behaviors introduced by Willems gives a good description of dynamicalsystems without reference to any particular representation of the system in terms of equations. Inthis note, we introduce a notion of behaviors that allows us to describe singular systems in a verynatural way. The...
This paper summarizes, clarifies, and corrects some aspects of the variational velocity methodfor the detection of limit cycles. After definitions and statements of the most important theoremsassociated with this method, some aspects of the proof of the main theorem are corrected andreworked. An...
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