On the Solutions of a Second Order Differential Equation Arising in the Theory of Resonant Oscillations in a Tank | Zendy

ByattSmith J. G. | Zendy

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On the Solutions of a Second Order Differential Equation Arising in the Theory of Resonant Oscillations in a Tank

Author(s) -

ByattSmith J. G.

Publication year - 1988

Publication title -

studies in applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 46

eISSN - 1467-9590

pISSN - 0022-2526

DOI - 10.1002/sapm1988792143

Subject(s) - bounded function , mathematics , mathematical analysis , connection (principal bundle) , initial value problem , order (exchange) , differential equation , partial differential equation , mathematical physics , physics , geometry , finance , economics

The properties of the solutions of the differential equation y ″ = y 2 − x 2 − c subject to the condition that y is bounded for all finite x discussed. The arguments of Holmes and Spence have been used by Ockendon, Ockendon, and Johnson to show that there are no solutions if c is large and negative. Numerically we find that solutions exist provided c is greater than a critical value c * and estimate this value to be c * = −…. As x tends to + ∞ the solutions are asymptotic to . The relation between A + and ϕ + are found analytically as A + → ∞. This problem arises as a connection problem in the theory of resonant oscillations of water waves.

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