Abstract
It is known that every positive solution of a one-dimensional Gel’fand problem can be written explicitly. In this paper, we give exact expressions of all the eigenvalues and eigenfunctions of the linearized eigenvalue problem at each solution. We study asymptotic behaviors of eigenvalues and eigenfunctions as the L∞-norm of the solution goes to infinity. We also study the problem u″ + λe−u = 0 and the associated linearized problem.
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