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- W2022384345 abstract "We consider the nonlinear Sturm–Liouville problem 1 $$ -u''(t) + f(u(t)) = lambda u(t),quad u(t) > 0, quad t in I := (0, 1),quad u(0) = u(1) = 0, $$ where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R + × L 2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u α with ‖ u α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u p satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ αp−1 h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by limu → ∞ uh′(u)." @default.
- W2022384345 created "2016-06-24" @default.
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- W2022384345 date "2006-04-07" @default.
- W2022384345 modified "2023-10-04" @default.
- W2022384345 title "Global behavior of the branch of positive solutions for nonlinear Sturm–Liouville problems" @default.
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- W2022384345 doi "https://doi.org/10.1007/s10231-006-0017-y" @default.
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