Positive solutions for logistic type quasilinear elliptic equations on RN

AbstractIn this paper, we consider positive solutions of the logistic type p-Laplacian equation −Δpu=a(x)|u|p−2u−b(x)|u|q−1u,x∈RN(N⩾2). We show that under rather general conditions on a(x) and b(x) for large |x|, the behavior of the positive solutions for large |x| can be determined. This is then used to show that there is a unique positive solution. Our results improve the corresponding ones in J. London Math. Soc. (2) 64 (2001) 107–124 and J. Anal. Math., in press

Test of CPT symmetry in cascade decays

Cascade mixing provides an elegant place to study the $B^0-\bar{B^0}$ mixing. We use this idea to study the CPT violation caused by $B^0-\bar{B^0}$ mixing. An approximation method is adopted to treat the two complex $B^0-\bar{B^0}$ mixing parameters $\theta$ and $\phi$. A procedure to extract the parameters $\theta$ and $\phi$ is suggested. The feasibility of exploring the CPT violation and determining of $\theta$ and $\phi$ in the future B-factories and LHC-B is discussed.Comment: Latex, 17 pages, some errors modifie

Robustness of Network of Networks with Interdependent and Interconnected links

Robustness of network of networks (NON) has been studied only for dependency coupling (J.X. Gao et. al., Nature Physics, 2012) and only for connectivity coupling (E.A. Leicht and R.M. D Souza, arxiv:0907.0894). The case of network of n networks with both interdependent and interconnected links is more complicated, and also more closely to real-life coupled network systems. Here we develop a framework to study analytically and numerically the robustness of this system. For the case of starlike network of n ER networks, we find that the system undergoes from second order to first order phase transition as coupling strength q increases. We find that increasing intra-connectivity links or inter-connectivity links can increase the robustness of the system, while the interdependency links decrease its robustness. Especially when q=1, we find exact analytical solutions of the giant component and the first order transition point. Understanding the robustness of network of networks with interdependent and interconnected links is helpful to design resilient infrastructures