Partial Differential Equations

Differential Equations

, Volume 48, Issue 8, pp 1119-1126

First online:

Dirichlet problem in the ball for an equation with a delta-like coefficient

  • A. B. AntonevichAffiliated withBelarus State University
  • , D. A. LyakhovAffiliated withBelarus State University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We study the Dirichlet problem in the ball for the Helmholtz equation with an additional term in the form of the product by the delta function. The additional term is approximated by the simplest integral expression, and the solution of the original equation is defined as the limit of solutions of the regularized equations. We obtain exact solutions depending on the chosen method of approximation.