Nonresonance conditions for a p-biharmonic operator with weight

Khalil Ben Haddouch, Zakaria El Allali, El Miloud Hssini, Najib Tsouli

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.

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