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71.
72.
Let x=(x',x')with x'∈Rk and x'∈R^N-k andΩbe a x'-symmetric and bounded domain in R^N(N≥2).We show that if 0≤a≤k-2,then there exists a positive constant C>0 such that for all x'-symmetric function u∈C0^∞(Ω)with∫Ω|■u(x)|^N-a|x'|^-adx≤1,the following uniform inequality holds1/∫Ω|x|^-adx∫Ωe^βa|u|N-a/N-a-1|x'|^-adx≤C,whereβa=(N-a)(2πN/2Γ(k-a/2)Γ(k/2)/Γ(k/2)r(N-a/2))1/N-a-1.Furthermore,βa can not be replaced by any greater number.As the application,we obtain some weighted Trudinger–Moser inequalities for x-symmetric function on Grushin space. 相似文献
73.
Jyoti P. Kharade Kishor D. Kucche 《Mathematical Methods in the Applied Sciences》2020,43(4):1938-1952
In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam-Hyers-Mittag-Leffler stability results for impulsive implicit Ψ-Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam-Hyers and generalized Ulam-Hyers stability are the specific cases of Ulam-Hyers-Mittag-Leffler stability. Extended version of the Gronwall inequality, abstract Gronwall lemma, and Picard operator theory are the primary devices in our investigation. We provide an example to illustrate the obtained results. 相似文献
74.
75.
Jung-Chan Chang 《Mathematical Methods in the Applied Sciences》2020,43(6):3586-3601
In this paper, by using some well-known inequalities and Schaefer fixed point theorem, we show existence results for impulsive Cauchy problems with nonlocal conditions. The compactness of solution sets can be shown in some certain conditions. Moreover, connectedness of solution sets to impulsive Cauchy problems is shown. 相似文献
76.
Tadahisa Funaki Yueyuan Gao Danielle Hilhorst 《Mathematical Methods in the Applied Sciences》2020,43(9):5860-5886
In this paper, we prove the existence and uniqueness of the entropy solution for a first-order stochastic conservation law with a multiplicative source term involving a -Brownian motion. After having defined a measure-valued weak entropy solution of the stochastic conservation law, we present the Kato inequality, and as a corollary, we deduce the uniqueness of the measure-valued weak entropy solution, which coincides with the unique weak entropy solution of the problem. The Kato inequality is proved by a doubling of variables method; to that purpose, we prove the existence and the uniqueness of the strong solution of an associated stochastic nonlinear parabolic problem by means of an implicit time discretization scheme; we also prove its convergence to a measure-valued entropy solution of the stochastic conservation law, which proves the existence of the measure-valued entropy solution. 相似文献
77.
Bollobás, Reed, and Thomason proved every 3‐uniform hypergraph ? with m edges has a vertex‐partition V()=V1?V2?V3 such that each part meets at least edges, later improved to 0.6m by Halsegrave and improved asymptotically to 0.65m+o(m) by Ma and Yu. We improve this asymptotic bound to , which is best possible up to the error term, resolving a special case of a conjecture of Bollobás and Scott. 相似文献
78.
Qian Jin Luo 《数学学报(英文版)》2020,36(6):711-722
Let B be the unit disc in R~2, H be the completion of C_0∞(B) under the norm■ .By the method of blow-up analysis and an argument of rearrangement with respect to the standard hyperbolic metric ■, we prove that, for any fixed■ ,the supremum■ .This is an analog of early results of Lu–Yang(Discrete Contin. Dyn. Syst., 2009) and Yang(Trans.Amer. Math. Soc., 2007), and extends those of Wang–Ye(Adv. Math., 2012) and Yang–Zhu(Ann.Global Anal. Geom., 2016). 相似文献
79.
80.
Reinhard Hochmuth 《Applicable analysis》2013,92(1-2):57-70
A new boundary integral equation formulation for the floating body problem, which is defined on a bounded domain and includes a hypersingular and a nonlocal part, is proved to satisfy a Gärding inequality. Under the assunlption of uniqueness it is shown, that an approximating sequence of related semidiscrete integral operators is uniformly bounded invertible. 相似文献