Bounded and L 2 -solutions to a second order nonlinear differential equation with a square integrable forcing term

Allan Kroopnick

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-3

Abstract:

This paper presents two theorems concerning the nonlinear differential equation x ″ + c ( t ) f ( x ) x ′ + a ( t , x ) = e ( t ) , where e ( t ) is a continuous square-integrable function. The first theorem gives sufficient conditions when all the solutions of this equation are bounded while the second theorem discusses when all the solutions are in L 2 [ 0 , ∞ ) .

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:865457

DOI: 10.1155/S0161171299225690

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