Periodic boundary value problems for n th-order ordinary differential equations with p -laplacian

Yuji Liu and Weigao Ge

Journal of Applied Mathematics, 2005, vol. 2005, 1-21

Abstract:

We prove existence results for solutions of periodic boundary value problems concerning the n th-order differential equation with p -Laplacian [ φ ( x ( n − 1 ) ( t ) ) ] ' = f ( t , x ( t ) , x ' ( t ) , ... , x ( n − 1 ) ( t ) ) and the boundary value conditions x ( i ) ( 0 ) = x ( i ) ( T ) , i = 0 , ... , n − 1 . Our method is based upon the coincidence degree theory of Mawhin. It is interesting that f may be a polynomial and the degree of some variables among x 0 , x 1 , ... , x n − 1 in the function f ( t , x 0 , x 1 , ... , x n − 1 ) is allowed to be greater than 1 .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:947920

DOI: 10.1155/JAM.2005.1

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