著者

Anello Giovanni

出版者

日本数学会函数方程式論分科会

雑誌

Funkcialaj Ekvacioj (ISSN:05328721)

巻号頁・発行日

vol.59, no.1, pp.113-122, 2016

被引用文献数

3

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Let Ω be a bounded domain in RN with smooth boundary. Let f: [0, + ∞[ → [0,+∞[, with f(0) = 0, be a continuous function such that, for some a > 0, the function ξ∈]0, +∞[ → ξ−2 · ∫0ξ f(t)dt is non increasing in ]0,a[. Finally, let α: <span style="text-decoration: overline">Ω</span> → [0,+∞[ be a continuous function with α(x) > 0, for all x ∈ Ω. We establish a necessary and sufficient condition for the existence of solutions to the following problem −Δu = λα(x)f(u) in Ω, u > 0 in Ω, u = 0 on ∂Ω, where λ is a positive parameter. Our result extends to higher dimension a similar characterization very recently established by Ricceri in the one dimensional case.