Wang, Shuyu.2009-03-202009-03-2019901990Source: Dissertation Abstracts International, Volume: 52-11, Section: B, page: 5870.9780315605862http://hdl.handle.net/10393/5772http://dx.doi.org/10.20381/ruor-10922This dissertation consists of two parts. First, we study some problems associated with reaction-diffusion equations with variables in finite-dimensional space. We investigate the positivity of solutions, the existence of positive invariant regions, and we also make some stability analysis. In part II, we study the Levy-Laplacian in infinite-dimensional space. We explore some properties of this Laplacian and solve some boundary value problems.125 p.Mathematics.Thesis