This book presents the main results and methods on inverse spectral problems for Sturm-Liouville differential operators and their applications. Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, electronics, geophysics, meteorology and other branches of natural sciences. Inverse problems also play an important role in solving non-linear evolution equations in mathematical physics. Interest in this subject has been increasing permanently because of the appearance of new important applications, resulting in intensive study of inverse problem theory all over the world.

http://www.gbv.de/dms/goettingen/326677410.pdf

Inverse Sturm-Liouville problems and their applications

This is a part of the Handbook of Differential Equations (A.
Canada, P. Drabek, A. Fonda, editors), where recent results in
the qualitative theory of half-linear differential equations
are presented.

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Half-linear differential equations

Boundary problems for ordinary differential equations with parameter in the boundary conditions

Boundary value problems for second-order differential equations on a finite inerval having a discontinuity in an interior point are studied. Completeness and expansion theorems are obtained and inverse problems are inverstigataed. For three classes of inverse problems the uniqueness theorems are proved. Necessary and sufficient conditions along with a procedure for the solution of the inverse problems are given.

Integral transforms connected with discontinuous boundary value problems

Boundary Eigenvalue Problems for Differential Equations Nη= λPη with λ-Polynomial Boundary Conditions

We consider the differential equation



on a finite interval I, where I contains m turning points, that is here, zeros of ϕ. Using asymptotic estimates proved by R. E. LANGER for solutions of (*) for intervals containing only one turning point we derive asymptotic estimates (for ρ → ) for a special fundamental system of solutions of (*) in I. The results obtained are fundamental for the investigation of eigenvalue problems defined by (*) and suitable boundary conditions.

Connection Formulas for Second Order Differential Equations with a Complex Parameter and Having an Arbitrary Number of Turning Points

Stone-reguläre Eigenwertprobleme

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Walter Eberhard

Papers

Connection Formulas for Second Order Differential Equations with a Complex Parameter and Having an Arbitrary Number of Turning Points

Stone-reguläre Eigenwertprobleme

On the distribution of the eigenvalues of a class of indefinite eigenvalue problems

Die Entwicklungen nach Eigenfunktionen irregulärer Eigenwertprobleme mit zerfallenden Randbedingungen

Nicht- S -hermitesche Rand- und Eigenwertprobleme