‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...

In this paper, by using the Euler-Maclaurin expansion for the zeta function and estimating the weight function effectively, we derive a strengthenment of a Hardy-Hilbert’s type inequality proved by W.Y. Zhong. As applications, some particular results are considered.

In this paper, we derive a nonlinear Picone identity to the pseudo p-Laplace operator, which contains some known Picone identities and removes a condition used in many previous papers. Some applications are given including a Liouville type theorem to the singular pseudo p-Laplace system, a Sturmian comparison principle to the pseudo p-Laplace equation, a new Hardy type inequality with weight an...

By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have been established.

*Correspondence: [email protected] 2Department of Construction and Information Engineering, Guangxi Modern Vocational Technology College, Hechi, Guangxi 547000, China Full list of author information is available at the end of the article Abstract We derive a strengthenment of a Hardy-Hilbert type inequality by using the Euler-Maclaurin expansion for the zeta function and estimating the weight...

An impulsive Cohen-Grossberg neural network with time-varying and S-type distributed delays and reaction-diffusion terms is considered. By using Hardy-Poincaré inequality instead of Hardy-Sobolev inequality or just the nonpositivity of the reaction-diffusion operators, under suitable conditions in terms of M-matrices which involve the reaction-diffusion coefficients and the dimension and size o...