Related papers: On the difference equation of the Poincare type

The main objective of this addendum to the mentioned article by Park is to provide some remarks on bifurcation theories for nonlinear partial differential equations (PDE) and their applications to fluid dynamics problems. We only wish to…

Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.

In this paper we prove discrete Poincar\'e inequalities that are uniform in the mesh size for the discrete de Rham complex of differential forms developed in [Bonaldi, Di Pietro, Droniou, and Hu, An exterior calculus framework for polytopal…

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Stokman (eds.), Cambridge University Press, 2021.

An proof of Poincare Duality with local coefficients and with compact support is provided. The proof does not require Sheaf Theory or anything equivalent and is thus more accessible for the general audience.

The content of this preprint together with additional material appears now in 0706.2154.

An error in the author's paper (Functiones et Approximatio, 37 . pp. 203-211) is corrected.

This note serves to provide additional details for the proof of Lemma 3.6 in our paper [Liu, Zhang and Zhang, Comm. Math. Sci., 3(2005), pp.201-218]. Moreover, we will also present an alternative, yet simpler, proof based on arguments in…

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.

Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…

A translation from Russian of the famous paper by Mark Krein "On the theory of symmetric polynomials" published in Math. Sb., vol. 40, no. 3, 1933, pp. 271-283.

One of the two basic theorems in [5] on the existence of solutions of PDEs is improved with the use of a group analysis type argument.

This paper is a complement of our recent works on the semilinear Tricomi equations in [8] and[9].

Here we outline a proof for the 4-dimensional smooth Poincare Conjecture.

Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…

This paper has been superseded by math.AG/0510287 and withdrawn by the author.

Analogues of JSJ decompositions were developed for Poincar\'e duality pairs in [19]. These decompositions depend only on the group. Our focus will be on describing the edge splittings of these decompositions more precisely. We use our…

We prove a formula relating the fermionic forms and the Poincare polynomials of quiver varieties associated to a finite quiver. Applied to quivers of type ADE, our result implies a version of the fermionic conjecture of Lusztig.