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

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  • Allan Kroopnick

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 , ∞ ) .

Suggested Citation

  • Allan Kroopnick, 1999. "Bounded and L 2 -solutions to a second order nonlinear differential equation with a square integrable forcing term," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 22, pages 1-3, January.
    • Handle: RePEc:hin:jijmms:865457
    DOI: 10.1155/S0161171299225690
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