Existence and Multiplicity of a Nonhomogeneous Polyharmonic Equation With Critical Exponential Growth in Even Dimension

Abstract

In this paper we study the existence of at least two positive weak solutions for an inhomogeneous fourth order equation with Navier boundary data involving nonlinearities of critical growth with a bifurcation parameter $\lambda$ in ${\mathbb{R}}^{2m}$. We establish here the lower and upper bound for $\lambda$ which determine multiplicity and non-existence respectively.