We prove some new Hardy type inequalities on the bounded domain with smooth boundary in the Carnot group. Several estimates of the first and second Dirich- let eigenvalues for the p-sub-Laplacian are established.
In this paper we prove some Liouville type results for the p-sub-Laplacian on the group of Heisenberg type. A strong maximum principle and a Hopf type principle concerning p-sub-Laplacian are established.
We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p 〉 2, -△p^u -= f（u） in R^2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The ex...We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p 〉 2, -△p^u -= f（u） in R^2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The existence of saddle solutions of the above problem was known only in dimensions 2m≥ 2p.展开更多
文摘We prove some new Hardy type inequalities on the bounded domain with smooth boundary in the Carnot group. Several estimates of the first and second Dirich- let eigenvalues for the p-sub-Laplacian are established.
文摘In this paper we prove some Liouville type results for the p-sub-Laplacian on the group of Heisenberg type. A strong maximum principle and a Hopf type principle concerning p-sub-Laplacian are established.
基金Supported by NSFC(No11001221)the Foundation of Shaanxi Province Education Department (No2010JK549)Zhejiang Provincial Natural Science Foundation of China(NoY6110118)
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11101134, 11371128） and the Young Teachers Program of Hunan University. The authors thank the anonymous referees for their valuable comments and suggestions.
文摘We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p 〉 2, -△p^u -= f（u） in R^2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The existence of saddle solutions of the above problem was known only in dimensions 2m≥ 2p.
