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2006 $L^q$ spectral asymptotics for nonlinear Sturm-Liouville problems
Tetsutaro Shibata
Differential Integral Equations 19(7): 773-783 (2006).

Abstract

We consider the nonlinear Sturm-Liouville problem $$ -u''(t) + f(u(t)) = \lambda u(t), \ \ u(t) > 0, \quad t \in I := (0, 1), \ \ u(0) = u(1) = 0, $$ where $\lambda > 0$ is an eigenvalue parameter. For better understanding of the global behavior of the branch of positive solutions in $\mbox{\bf R}_+ \times L^q(I)$ ($1 \le q \le \infty$), we establish precise asymptotic formulas for the eigenvalue $\lambda$ with respect to $\Vert u_\lambda\Vert_q$, where $u_\lambda$ is the unique solution associated with given $\lambda > \pi^2$.

Citation

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Tetsutaro Shibata. "$L^q$ spectral asymptotics for nonlinear Sturm-Liouville problems." Differential Integral Equations 19 (7) 773 - 783, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.34273
MathSciNet: MR2235894

Subjects:
Primary: 34L20
Secondary: 34L30 , 47J10

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 7 • 2006
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