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...

This paper deals with some extensions of Hardy-Hilbert’s inequality with the best constant factors by introducing two parameters λ and α and using the Beta function. The equivalent form and some reversions are considered.

[1] G. H. HARDY, J. E. LITTLEWOOD AND G. POLYA, Inequalities, Cambridge Univ. Press, Cambridge, 1995. [2] GAO MINGZHE, A Note on the Hardy-Hilbert Inequality, J. Math. Anal. Appl. Vol. 204, No. 1 (1996), 346–351. [3] GAO MINGZHE AND YANG BICHEN, on the Extended Hilbert’s Inequality, Proc. Amer. Math. Soc. Vol. 126, No. 3 (1998), 751–759. [4] W. H. GREUB, Linear Algebra, Springer Verlag, Berlin,...

Abstract By means of the weight functions, Hermite–Hadamard’s inequality, and techniques real analysis, a new more accurate reverse half-discrete Mulholland-type inequality involving one higher-order derivative function is given. The equivalent statements best possible constant factor related to few parameters, forms, several particular inequalities are provided. Another kind reverses also cons...

by using euler-maclaurin's summation formula and the way of real analysis, a more accurate multiplehilbert-type inequality and the equivalent form are given. we also prove that the same constantfactor in the equivalent inequalities is the best possible.

We prove some Hardy type inequalities related to quasilinear second order degenerate elliptic differential operators Lpu := −∇ ∗ L(|∇Lu| ∇Lu). If φ is a positive weight such that −Lpφ ≥ 0, then the Hardy type inequality c ∫ Ω |u| φp |∇Lφ| p dξ ≤ ∫

By means of the weight functions, idea introduced parameters, using transfer formula and Hermite–Hadamard’s inequality, a more accurate half-discrete multidimensional Hilbert-type inequality with homogeneous kernel as 1(x+||k−ξ||α)λ(x,λ>0) involving one multiple upper limit function is given, which new application inequalities. The equivalent conditions best possible constant factor related ...

In this paper, we provide a short account of the study of Hilbert-typeinequalities during the past almost 100 years by introducing multi-parametersand using the method of weight coefficients. A basic theorem of Hilbert-typeinequalities with the homogeneous kernel of −−degree and parameters is proved.