Spectra of fourth-order quasilinear problems

We are interested in spectra of the Dirichlet, Navier and Neumann boundary value problem for the fourth-order quasilinear equation(|u″|p−2u″)″=λ|u|p−2uin   [0,1],where λ∈R and p>1p>1. For p=2p=2 the equation reduces to the linear beam equation, u(4)=λuu(4)=λu. The operator on the left-hand side is often called a p-biharmonic operator. We introduce recent results on the properties of the spectra, and also an optimization algorithm which is useful for figuring them.