Abstract
We study a homogeneous partial differential equation and get its entire solutions represented in convergent series of Laguerre polynomials. Moreover, the formulae of the order and type of the solutions are established.
Highlights
Introduction and Main ResultsThe existence and behavior of global meromorphic solutions of homogeneous linear partial differential equations of the second order a0 ∂2u ∂t2 ∂2u ∂t∂z a2 ∂2u ∂z2 a3 ∂u ∂t a4 ∂u ∂z a6u1.1 where ak ak t, z are polynomials for t, z ∈ C2, have been studied by Hu and Yang 1
We will characterize the entire solutions of 1.5, which are related to Laguerre polynomials
Hu and Yang 2 established an analogue of Lindelof-Pringsheim theorem for the entire solution of PDE 1.2
Summary
0, 1.1 where ak ak t, z are polynomials for t, z ∈ C2, have been studied by Hu and Yang 1. Hu and Li 3 studied meromorphic solutions of homogeneous linear partial differential equations of the second order in two independent complex variables:. Equation 1.4 has a lot of entire solutions on C2 represented by Jacobian polynomials. Global solutions of some first-order partial differential equations or system were studied by Berenstein and Li 4 , Hu and Yang 5 , Hu and Li 6 , Li 7 , Li and Saleeby 8 , and so on. We concentrate on the following partial differential equation PDE t. We will characterize the entire solutions of 1.5 , which are related to Laguerre polynomials. The formulae of the order and type of the solutions are obtained
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