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Uniqueness of positive solutions for boundary value problems associated with indefinite ϕ-Laplacian-type equations
Open Mathematics ( IF 1.7 ) Pub Date : 2021-01-01 , DOI: 10.1515/math-2021-0003
Alberto Boscaggin 1 , Guglielmo Feltrin 2 , Fabio Zanolin 2
Affiliation  

This paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the ϕ -Laplacian equation ( ϕ ( u ′ ) ) ′ + a ( t ) g ( u ) = 0 , (\phi \left(u^{\prime} ))^{\prime} +a\left(t)g\left(u)=0, where ϕ is a homeomorphism with ϕ (0) = 0, a ( t ) is a stepwise indefinite weight and g ( u ) is a continuous function. When dealing with the p -Laplacian differential operator ϕ ( s ) = ∣ s ∣ p −2 s with p > 1, and the nonlinear term g ( u ) = u γ with γ ∈ R \gamma \in {\mathbb{R}} , we prove the existence of a unique positive solution when γ ∈ ]− ∞ \infty , (1 − 2 p )/( p − 1)] ∪ ] p − 1, + ∞ \infty [.

中文翻译:

与不定ϕ-Laplacian型方程有关的边值问题的正解的唯一性

本文为Neumann问题的正解和与ϕ -Laplacian方程()(u''))'+ a(t)g(u)= 0,(\ phi \ left( u ^ {\ prime}))^ {\ prime} + a \ left(t)g \ left(u)= 0,其中ϕ是o(0)= 0的同胚性,a(t)是逐步不确定的weight和g(u)是一个连续函数。当处理p -Laplacian微分算子ϕ(s)= ∣ s ∣ p -2 s(p> 1)和非线性项g(u)= uγ且γ∈R \ gamma \ in {\ mathbb {R }},我们证明了当γ∈] −∞\ infty,(1 − 2 p)/(p − 1)]∪] p − 1,+∞\ infty [。时,存在唯一的正解。
更新日期:2021-01-01
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