Displaying similar documents to “Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay”

A purely analytical lower bound for L ( 1 , χ )

Olivier Ramaré (2009)

Annales mathématiques Blaise Pascal

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We give a simple proof of L ( 1 , χ ) q 2 ω ( q ) when χ is an odd primitiv quadratic Dirichlet character of conductor q . In particular we do not use the Dirichlet class-number formula.

Gradient estimates for a nonlinear equation Δ f u + c u - α = 0 on complete noncompact manifolds

Jing Zhang, Bingqing Ma (2011)

Communications in Mathematics

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Let ( M , g ) be a complete noncompact Riemannian manifold. We consider gradient estimates on positive solutions to the following nonlinear equation Δ f u + c u - α = 0 in M , where α , c are two real constants and α > 0 , f is a smooth real valued function on M and Δ f = Δ - f . When N is finite and the N -Bakry-Emery Ricci tensor is bounded from below, we obtain a gradient estimate for positive solutions of the above equation. Moreover, under the assumption that -Bakry-Emery Ricci tensor is bounded from below and | f | is bounded...