Geodesic
Space of Solutions of Homogeneous Elliptic Equations
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 17-24

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This is the continuation of our paper [1] and includes the results promised there. As in [1], we consider a homogeneous elliptic equation in two variables. In [1] we showed that all solutions of such equations can be written in a specific form, viz. in the form of an infinite series in certain specific polynomials. Here we first establish that a common solution of any two positive powers of any two linearly independent, linear elliptic polynomials can be expressed as a polynomial (Lemma 2). 
Dubinsky, E.; Husain, T. Space of Solutions of Homogeneous Elliptic Equations. Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 17-24. doi: 10.4153/CMB-1971-004-2
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     title = {Space of {Solutions} of {Homogeneous} {Elliptic} {Equations}},
     journal = {Canadian mathematical bulletin},
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     year = {1971},
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     number = {1},
     doi = {10.4153/CMB-1971-004-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-004-2/}
}
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