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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.

Periodic singular problem with quasilinear differential operator

Irena Rachůnková, Milan Tvrdý (2006)

Mathematica Bohemica

We study the singular periodic boundary value problem of the form φ ( u ' ) ' + h ( u ) u ' = g ( u ) + e ( t ) , u ( 0 ) = u ( T ) , u ' ( 0 ) = u ' ( T ) , where φ is an increasing and odd homeomorphism such that φ ( ) = , h C [ 0 , ...

Periodic solutions for second order Hamiltonian systems

Qiongfen Zhang, X. H. Tang (2012)

Applications of Mathematics

By using the least action principle and minimax methods in critical point theory, some existence theorems for periodic solutions of second order Hamiltonian systems are obtained.

Periodic solutions for third order ordinary differential equations

Juan J. Nieto (1991)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we introduce the concept of upper and lower solutions for third order periodic boundary value problems. We show that the monotone iterative technique is valid and obtain the extremal solutions as limits of monotone sequences. We first present a new maximum principle for ordinary differential inequalities of third order that is interesting by itself.

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