Abstract
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.
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