Summing logarithmic expansions for singularly perturbed eigenvalue problems

摘要: Strong localized perturbations of linear and nonlinear eigenvalue problems in a bounded two-dimensional domain D are considered. The effects on an $\lambda _0 $ the Lapla-cian, fold point _{c0} problem, removing small subdomain $D_\epsilon $, “radius” $\epsilon from imposing condition boundary resulting hole, determined. Using method matched asymptotic expansions, it is shown that expansions eigenvalues points for these perturbed start with infinite series powers $( - 1/\log [ \epsilon d( \kappa ) ] )$. Here $d( )$ constant depends shape precise form hole. In each case, entire contained solution single related problem does not involve size or This stiff can be solved numerically...