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MATHEMATICA BOHEMICA, Vol. 121, No. 3, pp. 301-314, 1996
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On solvability of nonlinear operator equations and eigenvalues of homogeneous operators

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Vera Buryskova, Slavomir Burysek

* Vera Buryskova*, * Slavomir Burysek*, Department of Mathematics, Faculty of Mechanical Engineering, Czech Technical University Prague, Karlovo nam. 13, 121 35 Praha 2, Czech Republic

**Abstract:** Notions as the numerical range $W(S,T)$ and the spectrum $\sigma(S,T)$ of couple $(S,T)$ of homogeneous operators on a Banach space are used to derive theorems on solvability of the equation $Sx-\lambda Tx=y.$ Conditions for the existence of eigenvalues of the couple $(S,T)$ are given.

**Keywords:** Banach and Hilbert space, homogeneous, polynomial, symmetric, monotone operator, numerical range, spectrum, eigenvalue.

**Classification (MSC91):** 47H15

**Full text of the article:**

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