Multiple solutions of a fourth-order nonhomogeneous equation with critical growth in ℝ4

Abstract

In this article we study the existence of at least two positive weak solutions of an nonhomogeneous fourth-order Navier boundary-value problem involving critical exponential growth on a bounded domain in ℝ⁴, with a parameter λ > 0. We establish upper and lower bounds for λ, which determine multiplicity and non-existence of solutions.