Landau-type inequalities and -bounded solutions of neutral delay systems.

Günzler, Hans

Displaying similar documents to “Landau-type inequalities and $L^{p}$ -bounded solutions of neutral delay systems.”

New Orlicz variants of Hardy type inequalities with power, power-logarithmic, and power-exponential weights

Agnieszka Kałamajska, Katarzyna Pietruska-Pałuba (2012)

Open Mathematics

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We obtain Hardy type inequalities $\int_{0}^{\infty} M (ω (r) |u (r)|) ρ (r) d r ⩽ C_{1} \int_{0}^{\infty} M (|u (r)|) ρ (r) d r + C_{2} \int_{0}^{\infty} M (|u^{'} (r)|) ρ (r) d r,$ and their Orlicz-norm counterparts ${∥ω u∥}_{L^{M} (ℝ_{+}, ρ)} ⩽ {\tilde{C}}_{1} {∥u∥}_{L^{M} (ℝ_{+}, ρ)} + {\tilde{C}}_{2} {∥u^{'}∥}_{L^{M} (ℝ_{+}, ρ)},$ with an N-function M, power, power-logarithmic and power-exponential weights ω, ρ, holding on suitable dilation invariant supersets of C 0∞(ℝ+). Maximal sets of admissible functions u are described. This paper is based on authors’ earlier abstract results and applies them to particular classes of weights.

Differential inequalities

Szarski, Jacek

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Sufficient conditions for weighted Gabushin inequalities

Richard C. Brown, Don B. Hinton (1986)

Časopis pro pěstování matematiky

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Weighted inequalities for monotone and concave functions

Hans Heinig, Lech Maligranda (1995)

Studia Mathematica

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Characterizations of weight functions are given for which integral inequalities of monotone and concave functions are satisfied. The constants in these inequalities are sharp and in the case of concave functions, constitute weighted forms of Favard-Berwald inequalities on finite and infinite intervals. Related inequalities, some of Hardy type, are also given.