Precise Asymptotic Formulas for Semilinear Eigenvalue Problems |
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Authors: | T Shibata |
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Institution: | (1) Applied Mathematics Research Group, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan |
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Abstract: | . We consider the nonlinear Sturm-Liouville problem¶¶-u"(t) = | u(t) | p-1u(t) - lu(t), t ? I :=(0,1), u(0) = u(1) = 0 -u'(t) = \mid u(t)\mid^{p-1}u(t) - \lambda u(t), t \in I :=(0,1), u(0) = u(1) = 0 ,¶¶ where p > 1 and l ? R \lambda \in {\bf R} is an eigenvalue parameter. To investigate the global L2-bifurcation phenomena, we establish asymptotic formulas for the n-th bifurcation branch l = ln (a) \lambda = \lambda_n (\alpha) with precise remainder term, where a \alpha is the L2 norm of the eigenfunction associated with l \lambda . |
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