Nonlinear Elliptic Dirichlet and No-Flux Boundary Value Problems

This paper is devoted to establishing results for semilinear elliptic boundary value problems where the solvability of problems subject to {\it No Flux} boundary conditions follows from the solvability of related {\it Dirichlet} boundary value problems. Throughout it is assumed that the nonlinear perturbation terms are gradient dependent. An extension of $\mathit{\text{No-Flux}}$ problems is discussed, as well.