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Precise Spectral Asymptotics for Nonlinear Sturm–Liouville Problems

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Abstract:

We consider the nonlinear Sturm–Liouville problem-u″(t)+u(t)p=u(t), u(t)>0, tI≔(0, 1), u(0)=u(1)=0,where p>1 is a constant and >0 is an eigenvalue parameter. To understand the global structure of the bifurcation diagram in R+×L2(I) completely, we establish the asymptotic expansion of (α) (associated with eigenfunction uα with ‖uα2=α) as α→∞. We also obtain the corresponding asymptotics of the width of the boundary layer of uα as α→∞. © 2002 Elsevier Science (USA).

Document Type: Research Article

Affiliations: The Division of Mathematical and Information Sciences, Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan

Publication date: April 1, 2002

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