A class of maps related to the semilinear spectrum and its applications
by
Wenying Feng
Computer Science and Mathematics, Trent University, Peterborough, ON, Canada K9J 7B8

Abstract: In this paper, a class of nonlinear maps, the (a, q)-L-stable solvable maps for the Fredholm operator L, is introduced. Closely related to the spectrum of semilinear operators, the (a, q)-L-stable solvable maps are generalization of the (a, q)-stably solvable maps that was defined by Appell, Giorgieri and Väth previously. We prove properties for the new class of operators including the continuation principle and eigenvalues. We also show its application in the study of solvability for differential equations.

Date received: March 17, 2007