Semilinear problems involving nonlinear operators of monotone type

Abstract

This is a survey article on semilinear problems with a non-symmetric linear part and a nonlinear part of monotone type in real Hilbert spaces. We study the solvability of semilinear inclusions in the nonresonance and resonance cases. Semilinear systems consisting of semilinear equations of different types are discussed.

Keywords

• semilinear inclusion
• semilinear system
• operators of monotone type
• degree theory