Displaying similar documents to “Asymptotic behavior of positive solutions of a Dirichlet problem involving supercritical nonlinearities”

L estimates of solution for m -Laplacian parabolic equation with a nonlocal term

Pulun Hou, Caisheng Chen (2011)

Czechoslovak Mathematical Journal

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In this paper, we consider the global existence, uniqueness and L estimates of weak solutions to quasilinear parabolic equation of m -Laplacian type u t - div ( | u | m - 2 u ) = u | u | β - 1 Ω | u | α d x in Ω × ( 0 , ) with zero Dirichlet boundary condition in Ω . Further, we obtain the L estimate of the solution u ( t ) and u ( t ) for t > 0 with the initial data u 0 L q ( Ω ) ( q > 1 ) , and the case α + β < m - 1 .

A note on the number of solutions of the generalized Ramanujan-Nagell equation x 2 - D = p n

Yuan-e Zhao, Tingting Wang (2012)

Czechoslovak Mathematical Journal

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Let D be a positive integer, and let p be an odd prime with p D . In this paper we use a result on the rational approximation of quadratic irrationals due to M. Bauer, M. A. Bennett: Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. Ramanujan J. 6 (2002), 209–270, give a better upper bound for N ( D , p ) , and also prove that if the equation U 2 - D V 2 = - 1 has integer solutions ( U , V ) , the least solution ( u 1 , v 1 ) of the equation u 2 - p v 2 = 1 satisfies p v 1 , and D > C ( p ) , where C ( p ) is an effectively computable...

A note on splittable spaces

Vladimir Vladimirovich Tkachuk (1992)

Commentationes Mathematicae Universitatis Carolinae

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A space X is splittable over a space Y (or splits over Y ) if for every A X there exists a continuous map f : X Y with f - 1 f A = A . We prove that any n -dimensional polyhedron splits over 𝐑 2 n but not necessarily over 𝐑 2 n - 2 . It is established that if a metrizable compact X splits over 𝐑 n , then dim X n . An example of n -dimensional compact space which does not split over 𝐑 2 n is given.

Countable compactness and p -limits

Salvador García-Ferreira, Artur Hideyuki Tomita (2001)

Commentationes Mathematicae Universitatis Carolinae

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For M ω * , we say that X is quasi M -compact, if for every f : ω X there is p M such that f ¯ ( p ) X , where f ¯ is the Stone-Čech extension of f . In this context, a space X is countably compact iff X is quasi ω * -compact. If X is quasi M -compact and M is either finite or countable discrete in ω * , then all powers of X are countably compact. Assuming C H , we give an example of a countable subset M ω * and a quasi M -compact space X whose square is not countably compact, and show that in a model of A. Blass and S. Shelah...