Related papers: The Euler obstruction of a $1$-form on a determina…
A new technique for calculating the normal forms associated with the map restricted to the center manifold of a class of parameterized maps near the fixed point is given first. Then we show the Takens-Bogdanov point of delay differential…
In this paper we focus on the stochastic Euler-Poincar\'{e} equations with pseudo-differential/multiplicative noise. We first establish two new cancellation properties on pseudo-differential operators, which play a key role in energy…
We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in C^4, we…
The method exploits the contraction of space to systematically obtain compact solitary solutions. The latter is provided for the incompressible Euler and Navier-Stokes PDE. The nonlinear response of momentum advection is moved into a term…
In this paper, we consider the nonlinear $\Psi$-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of results. The acquired results are…
In the class of admissible weak solutions, we prove a weak-strong uniqueness result for the incompressible Euler equations assuming that the symmetric part of the gradient belongs to $L^1_{\rm loc}([0,+\infty);L^{\rm…
Small non-autonomous perturbations around an equilibrium of a nonlinear delayed system are studied. Under appropriate assumptions, it is shown that the number of $T$-periodic solutions lying inside a bounded domain $\Omega\subset \R^N$ is,…
We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant…
In this article we study a class of delay differential equations with infinite delay in weighted spaces of uniformly continuous functions. We focus on the integrated semigroup formulation of the problem and so doing we provide an spectral…
We consider one dimensional holomorphic foliations with isolated singularities that leave invariant a local complete intersection. We establish explicit formulas for the total GSV index of such foliations and obtain bounds for this index.…
Our aim in this paper is to study the Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. In particular, we prove, owing to proper approximations of the singular potential and a suitable notion of variational…
For an arbitrary convex function $\Psi:[1,\infty) \to [1,\infty)$, we consider uniqueness in the following two related extremal problems: Problem A boundary value problem: Establish the existence of, and describe the mapping $f$, achieving…
In this paper, we use Conley index theory to examine the Poincare index of an isolated invariant set. We obtain some limiting conditions on a critical point of a planar vector field to be an isolated invariant set. As a result we show the…
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
In this paper, we investigate the sufficient conditions for existence and uniqueness of solutions and {\delta}-Ulam-Hyers-Rassias stability of an impulsive fractional differential equation involving $\psi$-Hilfer fractional derivative.…
We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the…
Let pi: M^{ell+n} -> B^n be a submersion that presents a regular foliation by its fibers, and let S^n subset M be a closed embedded complementary submanifold, with f = pi|S: S -> B. We give two concise obstructions to keeping S everywhere…
We calculate the threshold singularities in one-dimensional models using the universal low-energy formfactors obtained in the framework of the non-linear Luttinger liquid model. We find the reason why the simplified picture of the impurity…
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…
We investigate the structure of fully non-linear P.D.E.'s in holomorphic functions, with emphasis on the functorial generalisation of so called "irregular" O.D.E.'s. Highlights are an implicit function theorem removing the perturbation…