Low Energy Solutions for the Semiclassical Limit of Schrodinger–Maxwell Systems

We show that the number of positive solutions of Schrodinger– Maxwell system on a smooth bounded domain depends on the topological properties of the domain. In particular we consider the Lusternik– Schnirelmann category and the Poincaré polynomial of the domain

Stable standing waves for a class of nonlinear Schroedinger-Poisson equations

We prove the existence of orbitally stable standing waves with prescribed $L^2$-norm for the following Schr\"odinger-Poisson type equation \label{intro} %{%{ll} i\psi_{t}+ \Delta \psi - (|x|^{-1}*|\psi|^{2}) \psi+|\psi|^{p-2}\psi=0 \text{in} \R^{3}, %-\Delta\phi= |\psi|^{2}& \text{in} \R^{3},%. when $p\in \{8/3\}\cup (3,10/3)$. In the case $3<p<10/3$ we prove the existence and stability only for sufficiently large $L^2$-norm. In case $p=8/3$ our approach recovers the result of Sanchez and Soler \cite{SS} %concerning the existence and stability for sufficiently small charges. The main point is the analysis of the compactness of minimizing sequences for the related constrained minimization problem. In a final section a further application to the Schr\"odinger equation involving the biharmonic operator is given

Tamoxifen in treatment of hepatocellular carcinoma: a randomised controlled trial

Background Results from small randomised trials on tamoxifen in the treatment of hepatocellular carcinoma (HCC) are conflicting, We studied whether the addition of tamoxifen to best supportive care prolongs survival of patients with HCC. Methods Patients with any stage of HCC were eligible, irrespective of locoregional treatment. Randomisation was centralised, with a minimisation procedure accounting for centre, evidence of disease, and time from diagnosis. Patients were randomly allocated best supportive care alone or in addition to tamoxifen, Tamoxifen was given orally, 40 mg per day, from randomisation until death. Results 496 patients from 30 institutions were randomly allocated treatment from January, 1995, to January, 1997. Information was available for 477 patients. By Sept 15, 1997, 119 (50%) of 240 and 130 (55%) of 237 patients had died in the control and tamoxifen arms, respectively. Median survival was 16 months and 15 months (p=0.54), respectively, No differences were found within subgroups defined by prognostic variables. Relative hazard of death for patients receiving tamoxifen was 1.07 (95% CI 0.83-1.39). Interpretation Our findings show that tamoxifen is not effective in prolonging survival of patients with HCC