Abstract

We consider an abstract Euler–Poisson–Darboux equation containing powers of an unbounded operator that is the generator of a Bessel operator function. Sufficient conditions for the unique solvability of the Dirichlet problem on the half-line are obtained. The question concerning the convergence of the solution to zero at infinity is investigated. Examples are given.

中文翻译：

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含无界算子幂的抽象欧拉-泊松-达布方程半线上的狄利克雷问题

摘要

我们考虑一个抽象的欧拉-泊松-达布方程，其中包含无界算子的幂，该算子是贝塞尔算子函数的生成器。得到了半线上狄利克雷问题唯一可解的充分条件。研究了无穷远解收敛到零的问题。给出了例子。