Justification of asymptotic expansions of the eigenvalues of nonselfadjoint singularly perturbed elliptic boundary value problems. (English. Russian original) Zbl 0618.35005

Math. USSR, Sb. 57, 317-349 (1987); translation from Mat. Sb., Nov. Ser. 129(171), No. 3, 307-337 (1986).
General boundary value problems for scalar elliptic PDE’s of the order 2m, with a small parameter \(\epsilon\) with higher derivatives (singular perturbed boundary value problem) and degenerating for \(\epsilon\to 0\) to a not selfadjoint boundary value problem of the order 2n, \(m>n>0\), are examined. Asymptotic distributions and their substantiations for eigenvalues, eigenvectors, and solutions are presented. Substantiations of the asymptotic expansions are based on a norm estimation of an inversion operator for the operator of the singular perturbed problem.
Reviewer: J.Smid


35B25 Singular perturbations in context of PDEs
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35J40 Boundary value problems for higher-order elliptic equations
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