A multiparameter semipositone fractional laplacian problem involving critical exponent

2019/05/24 by Dhanya, R., Tiwari, Sweta
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.10062

Abstract

In this paper we prove the existence of at least one positive solution for nonlocal semipositone problem of the type (P_λ^μ)\ (-Δ)^s u · amp;= · amp; λ(u^q-1)+μu^r in Ω
u · amp; · gt; · amp;0 in Ω
u · amp;≡ · amp;0 on \mathbb R^N∖Ω.. when the positive parameters λ and μ belongs to certain range. Here Ω⊂\mathbb R^N is assumed to be a bounded open set with smooth boundary, s∈ (0,1), N> 2s and 0λ₀. Now for each λ>λ₀, for all small 0

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