Quasilinear elliptic and parabolic partial differential equations with a derivative driving force.

摘要

This dissertation presents existence theorems for singular quasilinear and parabolic partial differential equations with a sublinear derivative forcing function at resonance.; In the first chapter we study the singular quasilinear partial differential equation and special functions at resonance in a weighted Hilbert space. In the last chapter we study at {dollar}{lcub}partial uoverpartial t{rcub} + Qu{dollar} where Qu is a quasilinear elliptic differential operator of order 2m. We establish the existence of weak solutions, which are periodic in the time variable t, at resonance. In both chapters we define the notion of a first eigenvalue for Q.