Nonresonance conditions for fourth order nonlinear boundary value problems

C. De Coster, C. Fabry and F. Munyamarere

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-16

Abstract:

This paper is devoted to the study of the problem u ( 4 ) = f ( t , u , u ′ , u ″ , u ‴ ) , u ( 0 ) = u ( 2 π ) , u ′ ( 0 ) = u ′ ( 2 π ) , u ″ ( 0 ) = u ″ ( 2 π ) , u ‴ ( 0 ) = u ‴ ( 2 π ) . We assume that f can be written under the form f ( t , u , u ′ , u ″ , u ‴ ) = f 2 ( t , u , u ′ , u ″ , u ‴ ) u ″ + f 1 ( t , u , u ′ , u ″ , u ‴ ) u ′ + f 0 ( t , u , u ′ , u ″ , u ‴ ) u + r ( t , u , u ′ , u ″ , u ‴ ) where r is a bounded function. We obtain existence conditions related to uniqueness conditions for the solution of the linear problem u ( 4 ) = a u + b u ″ , u ( 0 ) = u ( 2 π ) , u ′ ( 0 ) = u ′ ( 2 π ) , u ″ ( 0 ) = u ″ ( 2 π ) , u ‴ ( 0 ) = u ‴ ( 2 π ) .

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:401560

DOI: 10.1155/S0161171294001031

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