Existence of solutions to nonlinear elliptic equations

This dissertation is concerned with the existence of solutions to fully nonlinear elliptic equations of the form Au = Fu, where A is a differential operator acting on a subspace of the Sobolev space W1,p loc (?), p > 1, ? is a bounded domain in RN and F is an operator depending on lower order terms which also satisfies certain growth conditions. In our study, we use variational methods, fixed point theorems and, especially, sub-supersolution theorems. Our sub-supersolution theorems obtained are motivated by and are more general than those of Vy Le and Schmitt. With our approach, the operator F is allowed to be singular, to contain convection terms and to involve nonlocal terms.