8905936 Shivaji and Castro This project is concerned with questions of existence and multiplicity of solutions to nonlinear elliptic partial differential equations. The particular problems under investigation represent extensions of previous studies by mathematicians world-wide which have lead to fundamental advances in nonlinear functional analysis and applications. These mathematical problems arise in many areas of science and engineering. Examples include the study of enzyme systems, heat generation, solid mechanics, stellar structure, and chemical reaction theory.