Nonharmonic Solutions of the Laplace Equation

1. It is known that solutions of the Laplace equation $$\frac{{\partial ^2 {\text{u}}}}{{\partial {\text{x}}^2 }} + \frac{{\partial ^2 {\text{u}}}}{{\partial {\text{y}}^2 }} = 0$$ considered in the space of distributions (hyperfunctions) are always classical solutions called harmonic functions. In this paper we shall consider the Laplace equation in the space of so-called boehmians and show that there may appear solutions which are not classical. The boehmians, we are dealing with, are particular cases of the more general concept of generalized functions introduced in [1], p. 120. Here, they are defined by using delta-sequences.