Monotonicity constraints and supercritical Neumann problems

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Increasing radial solutions for Neumann problems without growth restrictions (2011, methodology): “These assumptions, which hold for f(u) = up, p > 1, play a crucial role in the approach of Serra and Tilli, who minimize the energy functional corresponding to (1.1) among nonnegative, radial and radially nondecreasing functions within the associated Nehari manifold.”