A class of nonlinear elliptic problems driven by p（x）-Laplacian with a nonsmooth locally Lipschitz potential is considered.By applying the version of the nonsmooth three-critical-point theorem,the existence of three...A class of nonlinear elliptic problems driven by p（x）-Laplacian with a nonsmooth locally Lipschitz potential is considered.By applying the version of the nonsmooth three-critical-point theorem,the existence of three solutions to the problems is proved.展开更多
We consider a Neumann problem driven by the(p,g)-Laplacian under the Landesman-Lazer type condition.Using the classical saddle point theorem and other classical results of the calculus of variations,we show that the p...We consider a Neumann problem driven by the(p,g)-Laplacian under the Landesman-Lazer type condition.Using the classical saddle point theorem and other classical results of the calculus of variations,we show that the problem has at least one nontrivial weak solution.展开更多
.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of....In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.展开更多
In this paper we prove the existence of an open interval （λ＇,λ＇） for each A in the interval a class of Neumann boundary value equations involving the （p1,…,pn）- Laplacian and depending on A admits at least th...In this paper we prove the existence of an open interval （λ＇,λ＇） for each A in the interval a class of Neumann boundary value equations involving the （p1,…,pn）- Laplacian and depending on A admits at least three solutions. Our main tool is a recent three critical points theorem of Averna and Bonanno [Topo1. Methods Nonlinear Anal. [1] （2003） 93-103].展开更多
As the rapid growth of mobile social networks,mobile peer-to-peer(P2P)communications and mobile edge computing(MEC)have been developed to reduce the traffic load and improve the computation capacity of cellular networ...As the rapid growth of mobile social networks,mobile peer-to-peer(P2P)communications and mobile edge computing(MEC)have been developed to reduce the traffic load and improve the computation capacity of cellular networks.However,the stability of social network is largely ignored in the advances of P2P and MEC,which is related to the social relations between users.It plays a vital role in improving the efficiency and reliability of traffic offloading service.In this paper,we integrate an edge node and the nearby P2P users as a mobile P2P social network and introduce the problem of adaptive anchored(k,r)-core to maintain the stability of multiple mobile P2P networks.It aims to adaptively select and retain a set of critical users for each network,whose participation is critical to overall stability of the network,and allocate certain resource for them so that the maximum number of users of all networks will remain engaged and the traffic of cellular network can be minimized.We called the retained users as anchor vertices.To address it,we devise a peer-edge-cloud framework to achieve the adaptive allocation of resources.We also develop a similarity based onion layers anchored(k,r)-core(S-OLAK)algorithm to explore the anchor vertices.Experimental results based on a real large-scale mobile P2P data set demonstrate the effectiveness of our method.展开更多
The Bogomolov multiplier B0 （G） of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality o...The Bogomolov multiplier B0 （G） of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality of the Bogomolov multiplier is an obstruction to Noether＇s problem. We show that if G is a central product of G1 and G2, regarding Ki ≤ Z（Gi）,i = 1,2, and θ ： G1 →G2 is a group homomorphism such that its restriction θ｜K1 ： K1 → K2 is an isomorphism, then the triviality of Bo（G1/K1）, Bo（G1） and B0（G2） implies the triviality of Bo（G）. We give a positive answer to Noether＇s problem for all 2-generator p-groups of nilpotency class 2, and for one series of 4-generator p-groups of nilpotency class 2 （with the usual requirement for the roots of unity）.展开更多
In this paper, we investigate a class of Dirichlet quasilinear elliptic systems involving the(p1(x), ···, pn(x))-Laplacian. Based on the general three critical points theorem of B. Ricceri, we prove the...In this paper, we investigate a class of Dirichlet quasilinear elliptic systems involving the(p1(x), ···, pn(x))-Laplacian. Based on the general three critical points theorem of B. Ricceri, we prove the existence of at least three weak solutions to the system.展开更多
基金supported by the National Natural Science Foundation of China(Nos.10971043 and 11001063)the Natural Science Foundation of Heilongjiang Province of China(No.A200803)
文摘A class of nonlinear elliptic problems driven by p（x）-Laplacian with a nonsmooth locally Lipschitz potential is considered.By applying the version of the nonsmooth three-critical-point theorem,the existence of three solutions to the problems is proved.
文摘We consider a Neumann problem driven by the(p,g)-Laplacian under the Landesman-Lazer type condition.Using the classical saddle point theorem and other classical results of the calculus of variations,we show that the problem has at least one nontrivial weak solution.
文摘.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.
文摘In this paper we prove the existence of an open interval （λ＇,λ＇） for each A in the interval a class of Neumann boundary value equations involving the （p1,…,pn）- Laplacian and depending on A admits at least three solutions. Our main tool is a recent three critical points theorem of Averna and Bonanno [Topo1. Methods Nonlinear Anal. [1] （2003） 93-103].
基金This work was supported by National Key Research and Development Program of China under Grant 2019YFB2101901 and 2018YFC0809803National Natural Science Foundation of China under Grant 61702364.
文摘As the rapid growth of mobile social networks,mobile peer-to-peer(P2P)communications and mobile edge computing(MEC)have been developed to reduce the traffic load and improve the computation capacity of cellular networks.However,the stability of social network is largely ignored in the advances of P2P and MEC,which is related to the social relations between users.It plays a vital role in improving the efficiency and reliability of traffic offloading service.In this paper,we integrate an edge node and the nearby P2P users as a mobile P2P social network and introduce the problem of adaptive anchored(k,r)-core to maintain the stability of multiple mobile P2P networks.It aims to adaptively select and retain a set of critical users for each network,whose participation is critical to overall stability of the network,and allocate certain resource for them so that the maximum number of users of all networks will remain engaged and the traffic of cellular network can be minimized.We called the retained users as anchor vertices.To address it,we devise a peer-edge-cloud framework to achieve the adaptive allocation of resources.We also develop a similarity based onion layers anchored(k,r)-core(S-OLAK)algorithm to explore the anchor vertices.Experimental results based on a real large-scale mobile P2P data set demonstrate the effectiveness of our method.
基金Supported by Grant No.RD-08-82/03.02.2016 of Shumen University
文摘The Bogomolov multiplier B0 （G） of a finite group G is defined as the subgroup of the Schur multiplier consisting of the cohomology classes vanishing after restriction to all abelian subgroups of G. The triviality of the Bogomolov multiplier is an obstruction to Noether＇s problem. We show that if G is a central product of G1 and G2, regarding Ki ≤ Z（Gi）,i = 1,2, and θ ： G1 →G2 is a group homomorphism such that its restriction θ｜K1 ： K1 → K2 is an isomorphism, then the triviality of Bo（G1/K1）, Bo（G1） and B0（G2） implies the triviality of Bo（G）. We give a positive answer to Noether＇s problem for all 2-generator p-groups of nilpotency class 2, and for one series of 4-generator p-groups of nilpotency class 2 （with the usual requirement for the roots of unity）.
基金supported by National Natural Science Foundation of China(No.10971202)
文摘In this paper, we investigate a class of Dirichlet quasilinear elliptic systems involving the(p1(x), ···, pn(x))-Laplacian. Based on the general three critical points theorem of B. Ricceri, we prove the existence of at least three weak solutions to the system.
