Ordinary p ‐Biharmonic Problems

The aim of this paper is to recall known results on boundary value problems for the quasilinear fourth order differential equation in one dimension 1$$(| u^{\prime\prime}\vert^{p-2}u^{\prime\prime})^{\prime\prime}=f(t,u),\quad t\in[0,1],$$ where p >1. The operator at the left‐hand side is often called a p ‐biharmonic operator which reduces to u (4) for p = 2. It is a fourth order analogue of the well‐known p ‐Laplacian. We discuss spectral properties of the corresponding eigenvalue problems, and existence and global bifurcation of solutions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)