Strong Comparison Principle for Radial Solutions of Quasi-Linear Equations

Let be either a ball or an annulus centered about the origin in N and p the usual p-Laplace operator in N. Let f1 f2 ∈ L1 loc be two radial functions on with f1 ≤ f2 f1 ≡ f2. Let b → be a non-decreasing continuous function. Let u1 u2 ∈ C1 β β ∈ 0 1 be any two radial weak solutions of − pui = b ui + fi in . We then show that u1 ≤ u2 in implies u1 < u2 in and also that appropriate versions of Hopf boundary point principle hold.