Maximum principles for fourth order nonlinear elliptic equations with applications

Abstract

The paper is devoted to prove maximum principles for a certain functionals defined for solution of the fourth order nonlinear elliptic equation. The maximum principle so obtained is used to prove the nonexistence of nontrivial solutions of the fourth order nonlinear elliptic equation with some zero boundary conditions. Hopf's maximum principle is the main ingredient. © Soc. Paran. de Mat.