Displaying similar documents to “Sets of extended uniqueness and σ -porosity”

Vector integral equations with discontinuous right-hand side

Filippo Cammaroto, Paolo Cubiotti (1999)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the integral equation u ( t ) = f ( I g ( t , z ) u ( z ) d z ) , with t I = [ 0 , 1 ] , f : 𝐑 n 𝐑 n and g : I × I [ 0 , + [ . We prove an existence theorem for solutions u L ( I , 𝐑 n ) where the function f is not assumed to be continuous, extending a result previously obtained for the case n = 1 .

Non-autonomous vector integral equations with discontinuous right-hand side

Paolo Cubiotti (2001)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the integral equation u ( t ) = f ( t , I g ( t , z ) u ( z ) d z ) , with t I : = [ 0 , 1 ] , f : I × n n and g : I × I [ 0 , + [ . We prove an existence theorem for solutions u L s ( I , n ) , s ] 1 , + ] , where f is not assumed to be continuous in the second variable. Our result extends a result recently obtained for the special case where f does not depend explicitly on the first variable t I .

Theoretical analysis of discrete contact problems with Coulomb friction

Tomáš Ligurský (2012)

Applications of Mathematics

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A discrete model of the two-dimensional Signorini problem with Coulomb friction and a coefficient of friction depending on the spatial variable is analysed. It is shown that a solution exists for any and is globally unique if is sufficiently small. The Lipschitz continuity of this unique solution as a function of as well as a function of the load vector f is obtained. Furthermore, local uniqueness of solutions for arbitrary > 0 is studied. The question of existence of locally Lipschitz-continuous...