Asymptotic behaviour of solutions of fourth order Dirichlet problems

On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate

A range of Hardy-like spaces of ordinary Dirichlet series, called the Dirichlet-Hardy spaces $\Hp^p$, $p \geq 1$, have been the focus of increasing interest among researchers following a paper of Hedenmalm, Lindqvist and Seip in Duke Math. J 86 (1997), 1-37. The Dirichlet series in these spaces converge on a certain half-plane, where one may also define the classical Hardy spaces $H^p$. In this paper, we compare the boundary behaviour of elements in $\Hp^p$ and $H^p$. Moreover, Carleson measures of the spaces $\Hp^p$ are studied. Our main result shows that for certain cases the following state…

关于带振荡项的非局部 Dirichlet 问题

On nonlocal Dirichlet problems with oscillating term

本文研究一类非局部分数阶 Dirichlet 问题，利用 Ricceri 变分原理，在非线性项于原点或无穷远处具有合适振荡行为时，证明了该问题存在无穷多个弱解。

The Third Boundary Value Problem of Potential Theory for the Exterior Ball and the Approximation behaviour of the solution; a Novel Open Problem

The paper is concerned with the interconnection of the boundary behaviour of the solutions of the exterior Dirichlet and Neumann problems of harmonic analysis for the three-dimensional unit ball with the corresponding behaviour of the associated ergodic inverse problems for the punched unlimited space. The basis is the theory of semigroups of linear operators mapping a Banach space $X$ into itself. The rates of approximation play a basic role. Another tool is a Drazin-like inverse operator $B$ for the infinitesimal generator $A$ of a semigroup that arises naturally in ergodic theory. This oper…

Bound-state asymptotic estimates for window-coupled Dirichlet strips and layers

We consider the discrete spectrum of the Dirichlet Laplacian on a manifold consisting of two adjacent parallel strips or planar layers coupled by a finite number N of windows in the common boundary. If the windows are small enough, there is just one isolated eigenvalue. We find upper and lower asymptotic bounds on the gap between the eigenvalue and the essential spectrum in the planar case, as well as for N=1 in three dimensions. Based on these results, we formulate a conjecture on the weak-coupling asymptotic behaviour of such bound states.