A critical exponent p_crit(α,N,λ) governs existence of classical solutions for p below it and nonexistence of weak solutions for p above it in the semilinear heat inequality with Hardy potential on the sphere.
Fujita, On the blowing up of solutions of the Cauchy problem forut = ∆u +u1+α, J
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Semilinear Heat Inequalities with a Hardy-Type Potential in an Exterior Geodesic Domain on $\mathbb{S}^N$
A critical exponent p_crit(α,N,λ) governs existence of classical solutions for p below it and nonexistence of weak solutions for p above it in the semilinear heat inequality with Hardy potential on the sphere.