Geodesic
Description of Entire Solutions of Eiconal Type Equations
Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 249-259

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DOI

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 ${{\mathbf{C}}^{2}}$ .
DOI : 10.4153/CMB-2011-080-8
Mots-clés : 32A15, 35F20, entire solution, eiconal equation, polynomial, transcendental function 
Chang, Der-Chen; Li, Bao Qin. Description of Entire Solutions of Eiconal Type Equations. Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 249-259. doi: 10.4153/CMB-2011-080-8
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     author = {Chang, Der-Chen and Li, Bao Qin},
     title = {Description of {Entire} {Solutions} of {Eiconal} {Type} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {249--259},
     year = {2012},
     volume = {55},
     number = {2},
     doi = {10.4153/CMB-2011-080-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-080-8/}
}
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