In this paper, we propose an elliptic algebra Aq,p;π̂(ĝl2) which is based on the relations RLL = LLR, where R and R are the dynamical R-maxtrices of A (1) 1 type face model with the elliptic moduli shifted by the center of the algebra. From the Ding-Frenkel correspondence , we find that its corresponding (Drinfeld) current algebra at level one is the algebra of screening currents for qdeformed V...

By using the elliptic analogue of the Drinfeld currents in the elliptic algebra Uq,p(ŝlN ), we construct a L-operator, which satisfies the RLL-relations characterizing the face type elliptic quantum group Bq,λ(ŝlN ). For this purpose, we introduce a set of new currents Kj(v) (1 ≤ j ≤ N) in Uq,p(ŝlN ). As in the N = 2 case, we find a structure of Uq,p(ŝlN ) as a certain tensor product of Bq,λ(ŝl...

A theoretical foundation for a generalization of the elliptic difference Painlevé equation to higher dimensions is provided in the framework of birational Weyl group action on the space of point configurations in general position in a projective space. By introducing an elliptic parametrization of point configurations, a realization of the Weyl group is proposed as a group of Cremona transforma...

In this paper we find explicit lower bounds for Dirichlet eigenvalues of a weighted quasilinear elliptic system of resonant type in terms of the eigenvalues of a single p-Laplace equation. Also we obtain asymptotic bounds by studying the spectral counting function which is defined as the number of eigenvalues smaller than a given value.

After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group Bq,λ(ŝlN ) by the elliptic algebra Uq,p(ŝlN ), we investigate a fusion of the vertex operators of Uq,p(ŝlN ). The basic generating functions Λj(z) (1 ≤ j ≤ N − 1) of the deformed WN algebra are derived explicitly.

We study the fractional p-Kirchhoff equation $$ \Big( a+b \int_{\mathbb{R}^N}{\int_{\mathbb{R}^N}} \frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}\, dx\, dy\Big) (-\Delta)_p^s u-\mu|u|^{p-2}u=|u|^{q-2}u, \quad x\in\mathbb{R}^N, where \((-\Delta)_p^s\) is p-Laplacian operator, a and b are strictly positive real numbers, \(s \in (0,1)\), \(1 < p< N/s,\) \(p< q< p^*_s-2\) with \(p^*_s=\frac{Np}{N-p...

Existence and bifurcation of positive solutions to a Kirchhoff type equation ⎧⎪⎨ ⎪⎩ − ( a + b ∫ Ω |∇u|2 ) u= νf (x,u), in Ω, u= 0, on ∂Ω are considered by using topological degree argument and variational method. Here f is a continuous function which is asymptotically linear at zero and is asymptotically 3-linear at infinity. The new results fill in a gap of recent research about the Kirchhoff ...