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• W2071156895 abstract "Let B⊂Rn (n⩾1) be a unit ball and D⊂Rm be a bounded domain. We study the global branch consisting of interior single-peak solutions of the elliptic Neumann problemΔu+λ(−u+up)=0in B,∂νu=0on ∂B and the monotonicity of the first eigenvalue along the branch for large λ, where1<p<pS:={n+2n−2,n⩾3,∞,n=1,2. When the domain is replaced with B×D, using this monotonicity, we show that the branch of solutions concentrating on {0}×D has secondary bifurcation points. For n=1 and p⩾2 an integer, we determine the global bifurcation diagram by showing the monotonicity of the time-map (the period function). The monotonicity of the first eigenvalue along the whole branch is also proved for n=1 and p=3." @default.
• W2071156895 created "2016-06-24" @default.
• W2071156895 creator A5020719725 @default.
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• W2071156895 date "2013-01-01" @default.
• W2071156895 modified "2023-10-01" @default.
• W2071156895 title "Monotonicity of the first eigenvalue and the global bifurcation diagram for the branch of interior peak solutions" @default.
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• W2071156895 doi "https://doi.org/10.1016/j.jde.2012.08.001" @default.
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