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Description of Entire Solutions of Eiconal Type Equations |
Canad. Math. Bull. 55(2012), 249-259
Published:2011-04-25
Printed: Jun 2012
Printed: Jun 2012
- Der-Chen Chang,
- Bao Qin Li,
Abstract
The paper describes entire solutions to the eiconal type non-linear partial differential
equations, which include the eiconal equations $(X_1(u))^2+(X_2(u))^2=1$ as special cases,
where
$X_1=p_1{\partial}/{\partial z_1}+p_2{\partial}/{\partial z_2}$,
$X_2=p_3{\partial}/{\partial z_1}+p_4{\partial}/{\partial z_2}$
are linearly independent operators with $p_j$ being arbitrary
polynomials in $\mathbf{C}^2$.
| Keywords: | entire solution, eiconal equation, polynomial, transcendental function |
| MSC Classifications: |
32A15 - Entire functions 35F20 - Nonlinear first-order equations |