On operators of monotone type in Banach spaces

In this dissertation we are investigating two types of problems. The first type involves the ranges of operators of monotone type which map reflexive Banach spaces into their duals. The main method here is degree theory. Recent results of Berkovits, Berkovits and Mustonen, and Schoneberg are extended and/or improved.

The second type involves the solvability of the equation: $Au - Tu$ + $Cu$ = $f$ under various assumptions of monotonicity and compactness on the operators A, T, and C. Our results extend and/or improve results obtained by Kesavan, Kartsatos and Mabry, and Milojevic.