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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.