Existence of positive super-solution of non linear biharmonic equation

Abstract

In this thesis, the existence of positive classical super solutions of non linear biharmonic equations of the certain problem is investigated on restricted domain. To do this, we considered non decreasing continu ous function by considering a certain non negative density fuction. To achieve our stated objectives, we applied a maximum principle based arguments which give explicit estimates on positive super solution that can easily be applied to get Liouville type results for positive super so lutions either in exterior or unbounded domains. The final result of the findings illustrate in an explicit way for the existince of positive super solutions of higher order specifically the fourth order. Therefore, the obtained results solve the complexity of determining the existence of positive super solutions for higher order partial differential equations.