arXiv subjects
Publications and source records attributed to Yongyang Jin.
In this paper we obtain optimal multipolar Rellich inequality for biharmonic Schrodinger operator with positive multi-singular potentials. Moreover, we prove the attainability of the best constant and the criticality of the biharmonic Schrodinger operator.
In this letter, we construct new meshy soliton structures by using two concrete (2+1)-dimensional integrable systems. The explicit expressions based on corresponding Cole-Hopf type transformations are obtained. Constraint equation ft+\sum_{j=1}^{N} h_j(y)f_{jx} = 0 shows that these meshy soliton structures can be linear or parabolic. Interaction between meshy soliton structure and Lump structure are also revealed.
We proved some optimal Hardy inequalities in RNwhich is closely related to multipolar Schrödinger operators with mean-value type potentials, these sharp inequalities imply some multipolar type Heisenberg inequalities. We also obtained someimproved multipolar Hardy inequalities on bounded domains, moreover, we got the range of the best Hardy constant for a specific Hardy inequality.
In this paper, we obtained the Dunkl analogy of classical Lp Hardy inequality for $p > N + 2γ$ with sharp constant $\left(\frac{p-N-2γ}{p}\right)^{p}$, where $2γ$ is the degree of weight function associated with Dunkl operators, and $L^p$ Hardy inequalities with distant function in some G-invariant domains. Moreover we proved two sharp Hardy-Rellich type inequalities for Dunkl operators.
Integrable couplings are associated with non-semisimple Lie algebras. In this paper, we propose a new method to generate new integrable systems through making perturbation in matrix spectral problems for integrable couplings, which is called the `completion process of integrable couplings'. As an example, the idea of construction is applied to the Ablowitz-Kaup-Newell-Segur integrable coupling. Each equation in the resulting hierarchy has a bi-Hamiltonian structure furnished by the component-trace identity.
Let $\mathbb G$ be a step-two nilpotent group of H-type with Lie algebra $\mathfrak G=V\oplus \mathfrak t$. We define a class of vector fields $X=\{X_j\}$ on $\mathbb G$ depending on a real parameter $k\ge 1$, and we consider the corresponding $p$-Laplacian operator $L_{p,k} u= \text{div}_X (|\na_{X} u|^{p-2} \na_X u)$. For $k=1$ the vector fields $X=\{X_j\}$ are the left invariant vector fields corresponding to an orthonormal basis of $V$, for $k=2$ and $\mathbb G$ being the Heisenberg group they are introduced by Greiner \cite{Greiner-cjm79}. In this paper we obtain the fundamental solution for the operator $L_{p,k}$ and as an application, we get a Hardy type inequality associated with $X$.