13,554 research outputs found
Multiple positive solutions of a Sturm-Liouville boundary value problem with conflicting nonlinearities
We study the second order nonlinear differential equation \begin{equation*}
u"+ \sum_{i=1}^{m} \alpha_{i} a_{i}(x)g_{i}(u) - \sum_{j=0}^{m+1} \beta_{j}
b_{j}(x)k_{j}(u) = 0, \end{equation*} where ,
are non-negative Lebesgue integrable functions defined in
, and the nonlinearities are
continuous, positive and satisfy suitable growth conditions, as to cover the
classical superlinear equation , with . When the positive
parameters are sufficiently large, we prove the existence of at
least positive solutions for the Sturm-Liouville boundary value
problems associated with the equation. The proof is based on the Leray-Schauder
topological degree for locally compact operators on open and possibly unbounded
sets. Finally, we deal with radially symmetric positive solutions for the
Dirichlet problems associated with elliptic PDEs.Comment: 23 pages, 6 PNG figure
Leptonic Decays at BABAR
We present recent results on leptonic B decays using data collected by the
BaBar detector at the PEP-II asymmetric-energy e+e- collider at the Stanford
Linear Accelerator Center. We report searches for the B -> tau nu decay, based
on two statistically independent data samples.Comment: 4 pages, 3 eps figures, Submitted for the SUSY07 proceeding
Lichnerowicz-type equations on complete manifolds
Under appropriate spectral assumptions we prove two existence results for
positive solutions of Lichnerowicz-type equations on complete manifolds. We
also give a priori bounds and a comparison result that immediately yields
uniqueness for certain classes of solutions. No curvature assumptions are
involved in our analysis.Comment: 33 pages, submitte
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