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Periodic boundary value problem of a fourth order differential inclusion

Marko Švec — 1997

Archivum Mathematicum

The paper deals with the periodic boundary value problem (1) L 4 x ( t ) + a ( t ) x ( t ) F ( t , x ( t ) ) , t J = [ a , b ] , (2) L i x ( a ) = L i x ( b ) , i = 0 , 1 , 2 , 3 , where L 0 x ( t ) = a 0 x ( t ) , L i x ( t ) = a i ( t ) L i - 1 x ( t ) , i = 1 , 2 , 3 , 4 , a 0 ( t ) = a 4 ( t ) = 1 , a i ( t ) , i = 1 , 2 , 3 and a ( t ) are continuous on J , a ( t ) 0 , a i ( t ) > 0 , i = 1 , 2 , a 1 ( t ) = a 3 ( t ) · F ( t , x ) : J × R {nonempty convex compact subsets of R }, R = ( - , ) . The existence of such periodic solution is proven via Ky Fan’s fixed point theorem.

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