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

Determination of f0−σf_0-\sigma mixing angle through Bs0→J/Ψ f0(980)(σ)B_s^0 \to J/\Psi~f_0(980)(\sigma) decays

We study $B_s^0 \to J/\psi f_0(980)$ decays, the quark content of $f_0(980)$ and the mixing angle of $f_0(980)$ and $\sigma(600)$. We calculate not only the factorizable contribution in QCD facorization scheme but also the nonfactorizable hard spectator corrections in QCDF and pQCD approach. We get consistent result with the experimental data of $B_s^0 \to J/\psi f_0(980)$ and predict the branching ratio of $B_s^0 \to J/\psi \sigma$. We suggest two ways to determine $f_0-\sigma$ mixing angle $\theta$. Using the experimental measured branching ratio of $B_s^0 \to J/\psi f_0(980)$, we can get the $f_0-\sigma$ mixing angle $\theta$ with some theoretical uncertainties. We suggest another way to determine $f_0-\sigma$ mixing angle $\theta$ using both of experimental measured decay branching ratios $B_s^0 \to J/\psi f_0(980) (\sigma)$ to avoid theoretical uncertainties.Comment: arXiv admin note: substantial text overlap with arXiv:0707.263