A Buzano type inequality for two Hermitian forms and applications

A Buzano type inequality for two nonnegative Hermitian forms is obtained. Applications to inequalities for norm and numerical radius of bounded linear operators in complex Hilbert spaces are given.     

具有N-各向异性拉普拉斯算子的超线性问题的先验界

通过改进Brezis和Merle的方法,结合Moser-Trudinger不等式,移动平面方法及比较原理,得到了方程-Q_Nu=f(u),u∈W_0~(1,N)(Ω)的正解的先验界,其中Ω是R~N中的一个有界光滑区域,非线性项f至多具有指数型增长.     

Bounds for Shannon and Zipf‐Mandelbrot entropies

Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy.     

The pseudomonotone polar for multivalued operators

In this work, we study the pseudomonotonicity of multivalued operators from the point of view of polarity, in an analogous way as the well-known monotone polar due to Martínez-Legaz and Svaiter, and the quasimonotone polar recently introduced by Bueno and Cotrina. We show that this new polar, adapted for pseudomonotonicity, possesses analogous properties to the monotone and quasimonotone polar, among which are a characterization of pseudomonotonicity, maximality and pre-maximality. Furthermore, we characterize the notion of D-maximal pseudomonotonicity introduced by Hadjisavvas. We conclude this work studying the connections between pseudomonotonicity, variational inequality problems and upper sign-continuity.     

A half-space projection method for solving generalized Nash equilibrium problems

The generalized Nash equilibrium problem (GNEP) is an n-person noncooperative game in which each player’s strategy set depends on the rivals’ strategy set. In this paper, we presented a half-space projection method for solving the quasi-variational inequality problem which is a formulation of the GNEP. The difference from the known projection methods is due to the next iterate point in this method is obtained by directly projecting a point onto a half-space. Thus, our next iterate point can be represented explicitly. The global convergence is proved under the minimal assumptions. Compared with the known methods, this method can reduce one projection of a vector onto the strategy set per iteration. Numerical results show that this method not only outperforms the known method but is also less dependent on the initial value than the known method.     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.     

Contraction of the proximal mapping and applications to the equilibrium problem

In this paper, we introduce a new definition of Lipschitz-type continuity of a bifunction. Using this definition, we prove the contraction of the proximal mapping and apply it to the equilibrium problem over the fixed-point set of a nonexpansive mapping. We present a new algorithm for this problem. Under classical conditions, the convergence of the algorithm is proved. Finally, we present some numerical results for the proposed algorithm.     

Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential

This note is a continuation of the work[17].We study the following quasilinear elliptic equations(■)where 1 p N,0 ≤μ ((N-p)/p)~p and Q ∈ L~∞(R~N).Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.     

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In this paper, the asymptotic behavior of the weak solution (u_t)_{t\ge0} to the non-local Cauchy problems as stated in (1) is considered. Only using lower bounds of jumping kernel J(x,y) for large |x-y|, it is obtained that \|u_t\|_p\le c(t)\|u_0\|_q with any 1\le q相似文献