Abstract
UDC 517.9We study the relationship between the second-order nonlinear ordinary differential equations and the Hardy inequality in grand Lebesgue spaces. In particular, we give a characterization of the Hardy inequality by using nonlinear ordinary differential equations in grand Lebesgue spaces.
Publisher
Institute of Mathematics National Academy of Sciences of Ukraine
Subject
General Earth and Planetary Sciences,General Engineering,General Environmental Science
Reference34 articles.
1. R. A. Bandaliyev, Connection of two nonlinear differential equations with a two-dimensional Hardy operator in weighted Lebesgue spaces with mixed norm, Electron. J. Different. Equat., 2016, 1 – 10 (2016).
2. R. A. Bandaliyev, P. Gorka, Hausdorff operator in Lebesgue spaces, Math. Inequal. Appl., 22, 657 – 676 (2019), https://doi.org/10.7153/mia-2019-22-45
3. P. R. Beesack, Hardy’s inequality and its extensions, Pacific J. Math., 11, 39 – 61 (1961).
4. P. R. Beesack, Integral inequalities involving a function and its derivatives, Amer. Math. Monthly, 78, 705 – 741 (1971), https://doi.org/10.2307/2318009
5. J. S. Bradley, The Hardy inequalities with mixed norms, Canad. Math. Bull., 21, 405 – 408 (1978), https://doi.org/10.4153/CMB-1978-071-7