Displaying similar documents to “On the range of a closed operator in an L 1 -space of vector-valued functions”

On quadratically integrable solutions of the second order linear equation

T. Chantladze, Nodar Kandelaki, Alexander Lomtatidze (2001)

Archivum Mathematicum

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Integral criteria are established for dim V i ( p ) = 0 and dim V i ( p ) = 1 , i { 0 , 1 } , where V i ( p ) is the space of solutions u of the equation u ' ' + p ( t ) u = 0 satisfying the condition + u 2 ( s ) s i d s < + .

The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems

Cristinel Mortici (2006)

Czechoslovak Mathematical Journal

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Let T be a γ -contraction on a Banach space Y and let S be an almost γ -contraction, i.e. sum of an ε , γ -contraction with a continuous, bounded function which is less than ε in norm. According to the contraction principle, there is a unique element u in Y for which u = T u . If moreover there exists v in Y with v = S v , then we will give estimates for u - v . Finally, we establish some inequalities related to the Cauchy problem.

Periodic boundary value problem of a fourth order differential inclusion

Marko Švec (1997)

Archivum Mathematicum

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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.