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Displaying similar documents to “Exact asymptotic behavior of singular values of a class of integral operators”

Some estimates for the first eigenvalue of the Sturm-Liouville problem with a weight integral condition

Maria Telnova (2012)

Mathematica Bohemica

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Let λ 1 ( Q ) be the first eigenvalue of the Sturm-Liouville problem y ' ' - Q ( x ) y + λ y = 0 , y ( 0 ) = y ( 1 ) = 0 , 0 < x < 1 . We give some estimates for m α , β , γ = inf Q T α , β , γ λ 1 ( Q ) and M α , β , γ = sup Q T α , β , γ λ 1 ( Q ) , where T α , β , γ is the set of real-valued measurable on 0 , 1 x α ( 1 - x ) β -weighted L γ -functions Q with non-negative values such that 0 1 x α ( 1 - x ) β Q γ ( x ) d x = 1 ( α , β , γ , γ 0 ) .

The natural operators lifting vector fields to ( J r T * ) *

Włodzimierz M. Mikulski (2000)

Archivum Mathematicum

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For integers r 2 and n 2 a complete classification of all natural operators A : T | M n T ( J r T * ) * lifting vector fields to vector fields on the natural bundle ( J r T * ) * dual to r -jet prolongation J r T * of the cotangent bundle over n -manifolds is given.

Transition from decay to blow-up in a parabolic system

Pavol Quittner (1998)

Archivum Mathematicum

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We show a locally uniform bound for global nonnegative solutions of the system u t = Δ u + u v - b u , v t = Δ v + a u in ( 0 , + ) × Ω , u = v = 0 on ( 0 , + ) × Ω , where a > 0 , b 0 and Ω is a bounded domain in n , n 2 . In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.