Applications of variational identities to quasilinear elliptic differential equations

This paper investigates quasilinear elliptic equations of the form div {g(x, del u)} + lambda f(x, u) - 0, x is an element of Omega, u = 0, x is an element of partial derivative Omega, where SZ is a bounded domain with smooth boundary whose geometry includes t hat of a starlike domain. We derive bounds for the solutions when f satisfi es a supercritical growth condition and g a subcritical growth condition. ( C) 2000 Elsevier Science Ltd. All rights reserved.