Abstract
The present paper is concerned with some properties of the resolvent kernel of the perturbed operator (−Δ)m on Rn, where 2m>n≧3, n is odd, for small values of the spectral parameter. Results are applied to asymptotics of solutions of corresponding parabolic problems as t→∞.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Eidus, D.: The principle of the limit amplitude, Russian Math. Surveys 24, No. 3, (1969), 97–167.
Gohberg, I.C., Sigal, E.I.: An operator generalization of the logarithmic residue theorem, Math. USSR Sbornik 13 (1971), 603–625.
Gohberg, I.C., Kaashock, M.A., Lay, D.C.: Equivalence, linearization and decomposition of holomorphic operator functions, Journal of Functional Analysis 28 (1978), 102–144.
Jensen, A., Kato, T.: Spectral properties of Schrödinger operators, Duke Math. Journal 46, No. 3 (1979), 583–611.
Murata, M.: Asymptotic expansion in time for solutions of Schrödinger-type equations, Journal of Functional Analysis 49(1982), 10–56.
Vainberg, B.R.: On the analytical properties of the resolvent for a certain class of operator-pencils, Math. USSR Sbornik 6 (1968), 241–273.
Vainberg, B.R.: On exterior elliptic problems polynomially depending on a spectral parameter, Math. USSR Sbornik 21 (1973) 221–239.
Author information
Authors and Affiliations
Additional information
Dedicated to the memory of David Milman
Rights and permissions
About this article
Cite this article
Eidus, D. Solutions of external boundary problems for small values of the spectral parameter. Integr equ oper theory 9, 47–59 (1986). https://doi.org/10.1007/BF01257061
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01257061