Abstract
AbstractFor a non-negative and non-trivial real-valued continuous functionhΩ× [0, ∞) such thath(x, 0) = 0 for allx∈Ω, we study the boundary-value problemwhereΩ⊆ ℝN,N⩾ 2, is a bounded smooth domain and Δp:= div(|Du|p–2DDu) is thep-Laplacian. This work investigates growth conditions onh(x, t) that would lead to the existence or non-existence of distributional solutions to (BVP). In a major departure from past works on similar problems, in this paper we do not impose any special structure on the inhomogeneous termh(x, t), nor do we require any monotonicity condition onhin the second variable. Furthermore,h(x, t) is allowed to vanish in either of the variables.
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