Abstract
Given a bounded domain Ω we consider local weak blow-up solutions to the equation Δ p u= g( x) f( u) on Ω. The non-linearity f is a non-negative non-decreasing function and the weight g is a non-negative continuous function on Ω which is allowed to be unbounded on Ω. We show that if Δ p w=− g( x) in the weak sense for some w∈W 1,p 0(Ω) and f satisfies a generalized Keller–Osserman condition, then the equation Δ p u= g( x) f( u) admits a non-negative local weak solution u∈W 1,p loc (Ω)∩C(Ω) such that u( x)→∞ as x→∂Ω. Asymptotic boundary estimates of such blow-up solutions will also be investigated.
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