Bandura A. Entire functions of several variables of bounded L-index in direction

A definition of a function of bounded L-index in direction are supposed. The several multidimensional analogues of corresponding criteria of boundedness l-index are proved. Besides we establish a connection between the functions of bounded L-index in direction and functions of bounded L-index and describe the set of directions such that the boundedness of L-index in these directions implies boundedness of L-index in all directions. The sufficient conditions of boundedness of L-index in direction of some Weierstrass canonical products are obtained. The growth and the boundedness of L-index direction of entire solutions of differential equations and their systems and investigated.