Geodesic
Intersection number and eigenvectors of quasilinear Hilbert--Schmidt operators
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002), pp. 604-621.

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For the spesial class of quasilinear operators a topologocal construction is described with the help of which existence theorems of normalized eigenvectors may be obtained. The construction is based on utilization of an intersection number of two Hilbert submanifolds one of which is generated by the given operator and another is anchanged. 
@article{JMAG_2002_9_a4,
     author = {Ya. M. Dymarskii},
     title = {Intersection number and eigenvectors of quasilinear {Hilbert--Schmidt} operators},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {604--621},
     publisher = {mathdoc},
     volume = {9},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2002_9_a4/}
}
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Ya. M. Dymarskii. Intersection number and eigenvectors of quasilinear Hilbert--Schmidt operators. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2002), pp. 604-621. http://geodesic.mathdoc.fr/item/JMAG_2002_9_a4/