Asymptotic Shape of Solutions to Nonlinear Eigenvalue Problems
نویسنده
چکیده
We consider the nonlinear eigenvalue problem −u′′(t) = f(λ, u(t)), u > 0, u(0) = u(1) = 0, where λ > 0 is a parameter. It is known that under some conditions on f(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→∞.
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