On a Class of Time Inhomogeneous Nonsingular Flows and Schrödinger Operators.
On a class of variational problems defined by polynomial Lagrangians
On a class of weighted function spaces and related pseudodifferential operators
On a connection with torsion zero
On a construction connecting Lie algebras with general algebras
On a coregular division of a differential space by an equivalence relation
On a critical point theory for minimal surfaces spanning a wire in Rn.
On a diffeological group realization of certain generalized symmetrizable Kac-Moody Lie algebras.
On a fourth order equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
On a Fourth Order Equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
On a fourth order superlinear elliptic problem.
On a free boundary problem for minimal surfaces.
On a functional equation satisfied by certain Dirichlet series
On a general difference Galois theory I
We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic , we attach its Galois group, which is a group of coordinate transformation.
On a general difference Galois theory II
We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.
On a generalization of Helmholtz conditions
Helmholtz conditions in the calculus of variations are necessary and sufficient conditions for a system of differential equations to be variational ‘as it stands’. It is known that this property geometrically means that the dynamical form representing the equations can be completed to a closed form. We study an analogous property for differential forms of degree 3, so-called Helmholtz-type forms in mechanics (), and obtain a generalization of Helmholtz conditions to this case.
On a generalized Calabi-Yau equation
Dealing with the generalized Calabi-Yau equation proposed by Gromov on closed almost-Kähler manifolds, we extend to arbitrary dimension a non-existence result proved in complex dimension .
On a horizontal structure on differentiable manifolds
On a Linearization Theorem of Sternberg for Germs of Diffeomorphisms.
On a local degree for a class of multi-valued vector fields in infinite dimensional Banach spaces.