Displaying similar documents to “Remarks on the uniqueness of second order ODEs

Two notes on eventually differentiable families of operators

Tomáš Bárta (2010)

Commentationes Mathematicae Universitatis Carolinae

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In the first note we show for a strongly continuous family of operators ( T ( t ) ) t 0 that if every orbit t T ( t ) x is differentiable for t > t x , then all orbits are differentiable for t > t 0 with t 0 independent of x . In the second note we give an example of an eventually differentiable semigroup which is not differentiable on the same interval in the operator norm topology.

Singular solutions for the differential equation with p -Laplacian

Miroslav Bartušek (2005)

Archivum Mathematicum

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In the paper a sufficient condition for all solutions of the differential equation with p -Laplacian to be proper. Examples of super-half-linear and sub-half-linear equations ( | y ' | p - 1 y ' ) ' + r ( t ) | y | λ sgn y = 0 , r > 0 are given for which singular solutions exist (for any p > 0 , λ > 0 , p λ ).

On the completeness of the system { t λ n log m n t } in C 0 ( E )

Xiangdong Yang (2012)

Czechoslovak Mathematical Journal

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Let E = n = 1 I n be the union of infinitely many disjoint closed intervals where I n = [ a n , b n ] , 0 < a 1 < b 1 < a 2 < b 2 < < b n < , lim n b n = . Let α ( t ) be a nonnegative function and { λ n } n = 1 a sequence of distinct complex numbers. In this paper, a theorem on the completeness of the system { t λ n log m n t } in C 0 ( E ) is obtained where C 0 ( E ) is the weighted Banach space consists of complex functions continuous on E with f ( t ) e - α ( t ) vanishing at infinity.