Pointwise Bounds and Blow-up for Nonlinear Polyharmonic Inequalities

الأصل · EN

We obtain results for the following question where m≥ 1 and n≥ 2 are integers. Question. For which continuous functions f [0,∞)→ [0,∞) does there exist a continuous function φ (0,1)→ (0,∞) such that every C²ᵐ nonnegative solution u(x) of 0 ≤ -Δᵐ u≤ f(u) in B₂(0){0}⊂ Rⁿ satisfies u(x) = O(φ(|x|)) as x→ 0 and what is the optimal such φ when one exists?