Asymptotic shape of solutions to nonlinear eigenvalue problems
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We consider the nonlinear eigenvalue problem
-u''(t) = ƒ(λ, u(t)), u > 0, u(0) = u(1) =0,
where λ > 0 is a parameter. It is known that under some conditions on ƒ(λ, u), the shape of the solutions associated with λ is almost 'box' when λ ≫ 1. The purpose of this paper is to study precisely the asymptotic shape of the solutions as λ → ∞ from a standpoint of L1-framework. To do this, we establish the asymptotic formulas for L1-norm of the solutions as λ → ∞.
CitationShibata, T. (2005). Asymptotic shape of solutions to nonlinear eigenvalue problems. Electronic Journal of Differential Equations, 2005(37), pp. 1-16.
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