Geodesic
On solvability of nonlinear operator equations and eigenvalues of homogeneous operators
Mathematica Bohemica, Tome 121 (1996) no. 3, pp. 301-314.

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Notions as the numerical range $W(S,T)$ and the spectrum $\s(S,T)$ of couple $(S,T)$ of homogeneous operators on a Banach space are used to derive theorems on solvability of the equation $Sx-lTx=y.$ Conditions for the existence of eigenvalues of the couple $(S,T)$ are given.
DOI : 10.21136/MB.1996.125984
Classification : 47H15, 47J05
Keywords: Banach and Hilbert space; homogeneous operator; polynomial operator; symmetric operator; monotone operator; numerical range; spectrum; eigenvalue 
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Burýšková, Věra; Burýšek, Slavomír. On solvability of nonlinear operator equations and eigenvalues of homogeneous operators. Mathematica Bohemica, Tome 121 (1996) no. 3, pp. 301-314. doi : 10.21136/MB.1996.125984. http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.125984/

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