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Zeitschrift für Analysis und ihre Anwendungen

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Volume 20, Issue 3, 2001, pp. 565–577
DOI: 10.4171/ZAA/1031

Published online: 2001-09-30

A Semilinear Furi-Martelli-Vignoli Spectrum

Jürgen Appell[1], Espedito De Pascale[2] and A. Vignoli[3]

(1) Universität Würzburg, Germany
(2) Università della Calabria, Arcavacata di Rende, Italy
(3) Università di Roma 'Tor Vergata', Italy

In this note we extend a spectrum which was introduced by Furi, Martelli and the third author in 1978 for continuous nonlinear maps $F$ to a certain new spectrum for a “semilinear pair” ($L, F$), with $L$ being a linear Fredholm operator of index zero, and $F$ being nonlinear and continuous.

Keywords: Fredholm operator, continuous nonlinear operator, quasibounded nonlinear operator, measure of non-compactness, $\alpha$-contractive nonlinear operator, nonlinear spectrum, semilinear spectrum, coincidence degree, periodic solution

Appell Jürgen, De Pascale Espedito, Vignoli A.: A Semilinear Furi-Martelli-Vignoli Spectrum. Z. Anal. Anwend. 20 (2001), 565-577. doi: 10.4171/ZAA/1031