Semilinear equations with discrete spectrum

Alfonso Castro
Harvey Mudd College

This will be introductory presentation of results and techniques on the solvability of equations of the form L(u) + N(u) =0

where L is a linear operator with discrete spectrum. The role of the interaction of the spectrum of N'(u) with respect to the spectrum of L will be emphasized. Basic examples are given when L is the Laplacian operator, D’Alembert’s operator, and integral operators.