Boundedness of the L-index in a direction of entire solutions of second order partial differential equation

We construct a continuous function L : C-2 -> (0, +infinity)(2) such that every entire solution of a certain second order partial differential equation has bounded L-index in a direction b - (b(1); b(2)) is an element of C-2 \ {0}. On the other hand, the entire bivariate function F(z(1), z(2)) = cos root z(1)z(2) is a solution of this equation. The function F has unbounded index in each direction b is an element of C-2 \ {0}. The constructed function L is a full solution of a problem posed by A. A. Kondratyuk's in 2007 about the existence of the function L with specified properties. We also suggest a continuous function L-1 : C-2 -> (0, +infinity)(2) such that the function F has bounded L-1-index in every direction b is an element of C-n \ {0}.