Applications of variational identities to quasilinear elliptic differential equations

This paper investigates quasilinear elliptic equations of the form div g (x, ▽u) + λ f(x, u) = 0, x ∈ Ω, u = 0, x ∈ ∇Ω, where Ω is a bounded domain with smooth boundary whose geometry includes that of a starlike domain. We derive bounds for the solutions when f satisfies a supercritical growth condition and g a subcritical growth condition.