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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 BVP with φ -Laplacian and impulses

Vladimír Polášek (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The paper deals with the impulsive boundary value problem d d t [ φ ( y ' ( t ) ) ] = f ( t , y ( t ) , y ' ( t ) ) , y ( 0 ) = y ( T ) , y ' ( 0 ) = y ' ( T ) , y ( t i + ) = J i ( y ( t i ) ) , y ' ( t i + ) = M i ( y ' ( t i ) ) , i = 1 , ... m . The method of lower and upper solutions is directly applied to obtain the results for this problems whose right-hand sides either fulfil conditions of the sign type or satisfy one-sided growth conditions.

Periodic problems for ODEs via multivalued Poincaré operators

Lech Górniewicz (1998)

Archivum Mathematicum

We shall consider periodic problems for ordinary differential equations of the form x ' ( t ) = f ( t , x ( t ) ) , x ( 0 ) = x ( a ) , where f : [ 0 , a ] × R n R n satisfies suitable assumptions. To study the above problem we shall follow an approach based on the topological degree theory. Roughly speaking, if on some ball of R n , the topological degree of, associated to (), multivalued Poincaré operator P turns out to be different from zero, then problem () has solutions. Next by using the multivalued version of the classical Liapunov-Krasnoselskǐ guiding potential...

Periodic solution to a multispecies predator-prey competition dynamic system with Beddington-DeAngelis functional response and time delay

Xiaojie Lin, Zengji Du, Yansen Lv (2013)

Applications of Mathematics

In this paper, we are concerned with a delayed multispecies competition predator-prey dynamic system with Beddington-DeAngelis functional response. Some sufficient conditions which guarantee the existence of a positive periodic solution for the system are obtained by applying the Mawhin coincidence theory. The interesting thing is that the result is related to the delays, which is different from the corresponding ones known from literature (the results are delay-independent).

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