Precise Asymptotics for Bifurcation Curve of Nonlinear Ordinary Differential Equation
Keyword(s):
We study the following nonlinear eigenvalue problem −u″(t)=λf(u(t)),u(t)>0,t∈I:=(−1,1),u(±1)=0, where f(u)=log(1+u) and λ>0 is a parameter. Then λ is a continuous function of α>0, where α is the maximum norm α=∥uλ∥∞ of the solution uλ associated with λ. We establish the precise asymptotic formula for λ=λ(α) as α→∞ up to the third term of λ(α).
1989 ◽
Vol 41
(2)
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pp. 321-340
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1989 ◽
Vol 49
(3)
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pp. 237-245
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2009 ◽
Vol 79-82
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pp. 1205-1208
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1993 ◽
Vol 1
(3)
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