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

Eberhard W. | Zendy; Freiling G. | Zendy; Schneider A. | Zendy

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

Author(s) -

Eberhard W.,

Freiling G.,

Schneider A.

Publication year - 1994

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19941650114

Subject(s) - mathematics , connection (principal bundle) , eigenvalues and eigenvectors , interval (graph theory) , order (exchange) , turning point , differential equation , mathematical analysis , point (geometry) , boundary value problem , differential (mechanical device) , boundary (topology) , combinatorics , geometry , period (music) , physics , finance , quantum mechanics , acoustics , engineering , economics , aerospace engineering

We consider the differential equation\documentclass{article}\pagestyle{empty}\begin{document}$ - u '' + \chi (x)u = \rho ^2 \phi ^2 (x)u $\end{document} 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.

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