Eckhaus W Matched asymptotic expansions and singular perturbation. North Holland Publishing Company, Amsterdam. Eckhaus W Asymptotic analysis of singular perturbations, studies in mathematics and its applications, vol 9. North-Holland Publishing Co. Duke Math J — Geng FZ A novel method for solving a class of singularly perturbed boundary value problems based on reproducing kernel method. Appl Math Comput 8 — Geng FZ, Cui MG Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space. Appl Math Comput — Hinch EJ Perturbation methods.
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Fife , Semi-linear elliptic boundary value problems with small parameter. Centre, 98 , Amsterdam, Geel and E. De Jager , Hyperbolic singular perturbations of non-linear first order differential equations ; Differential Equations and Applications, Proceedings 3rd Scheveningen Conf.
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Nonlinear Singular Perturbation Phenomena: Theory and Applications
Centre, Amsterdam, Grasman and B. Matkovsky A variational approach to singularly perturbed, boundary value problems for ordinary and partial differential equations with turning points , SIAM J. N De Groen , Spectral properties of second order singularly perturbed boundary value problems with turning points , J.
Ecole Norm. Harris , Singular perturbations of two point boundary problems for systems of ordinary differential equations , Arch. Harris , Singular perturbations of two point boundary problems. Van Harten , Singularly perturbed non-linear 2nd order elliptic boundary value problems , Thesis, University of Utrecht, In this chapter we recall, with more details, properties of unbounded symmetric and self-adjoint operators and their connection with quadratic forms. We give a brief review of some standard facts on the extension theory of symmetric operators and the general theory of quadratic forms.
In particular, we formulate and prove the theorem that gives the basic criterion for self-adjointness.
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These facts will be used in the sequel. We recall also the well-known theorems on operator representations of quadratic forms. A more extensive treatment of the theory can be found in the well-known books by N. Akhiezer and I.
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Glazman , by T. Kato , and by M. Reed and B. Simon [, ]. There are numerous works devoted to the theory of extension of symmetric operators, were properties of extended operators are described.
Here we refer only to some sources that have influenced our research in this area: [28, 32, 34, 35, 39, 45, 54, 55, 64, 65, 68, 70, 71, 73, 75, 82, 91, 92, , , , , , ]. A considerable part of functional analysis, including the theory of linear operators, particularly the spectral theory, cannot be presented successively without the notion of a rigged Hilbert space.