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Displaying 5461 – 5480 of 11160

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On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions

Enrico Priola (1999)

Studia Mathematica

We study a new class of Markov type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space E. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.

On a class of nonlinear problems involving a p ( x ) -Laplace type operator

Mihai Mihăilescu (2008)

Czechoslovak Mathematical Journal

We study the boundary value problem - d i v ( ( | u | p 1 ( x ) - 2 + | u | p 2 ( x ) - 2 ) u ) = f ( x , u ) in Ω , u = 0 on Ω , where Ω is a smooth bounded domain in N . Our attention is focused on two cases when f ( x , u ) = ± ( - λ | u | m ( x ) - 2 u + | u | q ( x ) - 2 u ) , where m ( x ) = max { p 1 ( x ) , p 2 ( x ) } for any x Ω ¯ or m ( x ) < q ( x ) < N · m ( x ) ( N - m ( x ) ) for any x Ω ¯ . In the former case we show the existence of infinitely many weak solutions for any λ > 0 . In the latter we prove that if λ is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a 2 -symmetric version for even functionals...

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