Related papers: A Hopf type lemma for fractional equations
We construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of…
This paper provides motivation as well as a method of construction for Hopf algebras, starting from an associative algebra. The dualization technique involved relies heavily on the use of Sweedler's dual.
In this paper, we consider an equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in systems of functional differential equations respecting $\Gamma \times S^1$-spatial symmetries. The existence of branches…
We prove a nonlocal, nonlinear commutator estimate concerning the transfer of derivatives onto testfunctions. For the fractional $p$-Laplace operator it implies that solutions to certain degenerate nonlocal equations are higher…
Motivated by models that arise in controlled ship maneuvering, we analyze Hopf bifurcations in systems with piecewise smooth nonlinear part. In particular, we derive explicit formulas for the generalization of the first Lyapunov coefficient…
We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.
n^{th} root of a Lie algebra and its dual (that is fractional supergroup) based on the permutation group $S_n$ invariant forms are formulated in the Hopf algebra formalism. Detailed discussion of $S_3$-graided $sl(2)$ algebras is done.
We investigate variational methods for finding approximate solutions to the Fokker-Planck equation, especially in cases lacking detailed balance. These schemes fall into two classes: those in which a Hermitian operator is constructed from…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
We derive recursive equations for the characteristic numbers of rational nodal plane curves with at most one cusp, subject to point conditions, tangent conditions and flag conditions, developing techniques akin to quantum cohomology on a…
In this paper, we define a Hopf algebra structure on the vector space spanned by packed words using a selection-quotient coproduct. We show that this algebra is free on its irreducible packed words. Finally, we give some brief explanations…
This paper present a numerical method for solving nonlinear Fredholm integral equations. The method is based upon Newton type approximations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
We prove that extension groups in strict polynomial functor categories compute the rational cohomology of classical algebraic groups. This result was previously known only for general linear groups. We give several applications to the study…
We propose an algebraic study of the simple graph isomorphism problem. We define a Hopf algebra from an explicit realization of its elements as formal power series. We show that these series can be evaluated on graphs and count occurrences…
We provide some versions of the Zaremba-Hopf-Oleinik boundary point lemma for general elliptic and parabolic equations in divergence form under the sharp requirements on the coefficients of equations and on the boundaries of domains.
The study of the pentagon (fusion) equation leds to the Structure and the Classification theorem for finite dimenasional Hopf algebras: there exists a one to one correspondence between the set of types of n-dimensional Hopf algebtras and…
The paper concerns singular solutions of nonlinear elliptic equations, which include removable singularities for viscosity solutions, a strengthening of the Hopf Lemma including parabolic equations, Strong maximum principle and Hopf Lemma…
A type of fractional derivative, referred to as \alpha-derivative, is studied. The \alpha-derivative of fractional type obeys Leibnitz rule. Based on the definition of \alpha-derivative the operations of analysis and differential geometry…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
In this note we treat the equations of fractional elasticity. After establishing well-posedness, we show a compactness result related to the theory of homogenization. For this, a previous result in (abstract) homogenization theory of…