Asymptotic Behavior of Solution to Nonlinear Eigenvalue Problem

Tetsutaro Shibata
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Tetsutaro Shibata: Laboratory of Mathematics, School of Engineering, Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

Mathematics, 2020, vol. 8, issue 11, 1-6

Abstract: We study the following nonlinear eigenvalue problem: − u ″ ( t ) = λ f ( 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 = ? u λ ? ∞ of the solution u λ associated with λ . We establish the precise asymptotic formula for L 1 -norm of the solution ? u α ? 1 as α → ∞ up to the second term and propose a numerical approach to obtain the asymptotic expansion formula for ? u α ? 1 .

Keywords: asymptotic expansion; L 1 -norm of the solution; nonlinear eigenvalue problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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