Functional Analysis Based Methods on Existence and Uniqueness Problems for Partial Differential Equations

Abstract

In this study, we considered existence and uniqueness problems for partial differential . equations. . We used functional analysis techniques, where a partial differential equation is regarded as an operator on an appropriate Hilbert space. This Hilbert space is in fact a Sobolev space. In particular, we have dealt with two me/thods, variation methods and energy integral method. We have illustrated the techniques with some examples.