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Asymptotics for quasilinear elliptic non-positone problems

Zuodong YangQishao Lu — 2002

Annales Polonici Mathematici

In the recent years, many results have been established on positive solutions for boundary value problems of the form - d i v ( | u ( x ) | p - 2 u ( x ) ) = λ f ( u ( x ) ) in Ω, u(x)=0 on ∂Ω, where λ > 0, Ω is a bounded smooth domain and f(s) ≥ 0 for s ≥ 0. In this paper, a priori estimates of positive radial solutions are presented when N > p > 1, Ω is an N-ball or an annulus and f ∈ C¹(0,∞) ∪ C⁰([0,∞)) with f(0) < 0 (non-positone).

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