ASYMPTOTIC SHAPE OF SOLUTIONS TO NONLINEAR EIGENVALUE PROBLEMS

We consider the nonlinear eigenvalue problem -u ''(t) = f(lambda, u(t)), u>0, u(0) = u(1) = 0, where lambda > 0 is a parameter. It is known that under some conditions on f(lambda, u), the shape of the solutions associated with lambda is almost 'box' when lambda >> 1. The purpose of this paper is to study precisely the asymptotic shape of the solutions as lambda -> infinity from a standpoint of L-1-framework. To do this, we establish the asymptotic formulas for L-1-norm of the solutions as lambda -> infinity.