Nonresonance conditions for a p-biharmonic operator with weight

Abstract

This work is devoted to study two nonlinear problems of fourth
order governed by the p-biharmonic operators in nonresonance
cases. In the first problem we establish the nonresonance part of
the Fredholm's alternative, the second  is a nonresonance problem
relative to the first eigensurface for the spectrum of the
operator $\Delta^{2}_{p} u + 2\beta . \nabla (|\Delta
u|^{p-2}\Delta u) + |\beta|^{2}|\Delta u|^{p-2}\Delta u$, where
$\beta\in \mathbb{R}^{N}$ under Navier boundary conditions.