A new critical curve for the Lane-Emden system

We study stable positive radially symmetric solutions for the Lane-Emden system $-\Delta u=v^p$ in $\R^N$, $-\Delta v=u^q$ in $\R^N$, where $p,q\geq 1$. We obtain a new critical curve that optimally describes the existence of such solutions.Comment: 13 pages, 1 figur

Asymptotic behaviour of a semilinear elliptic system with a large exponent

Consider the problem \begin{eqnarray*} -\Delta u &=& v^{\frac 2{N-2}},\quad v>0\quad {in}\quad \Omega, -\Delta v &=& u^{p},\:\:\:\quad u>0\quad {in}\quad \Omega, u&=&v\:\:=\:\:0 \quad {on}\quad \partial \Omega, \end{eqnarray*} where $\Omega$ is a bounded convex domain in $\R^N,$ $N>2,$ with smooth boundary $\partial \Omega.$ We study the asymptotic behaviour of the least energy solutions of this system as $p\to \infty.$ We show that the solution remain bounded for $p$ large and have one or two peaks away form the boundary. When one peak occurs we characterize its location.Comment: 16 pages, submmited for publicatio

Adjuvant capecitabine in triple negative breast cancer patients with residual disease after neoadjuvant treatment: real-world evidence from CaRe, a multicentric, observational study

Background: In triple negative breast cancer patients treated with neoadjuvant chemotherapy, residual disease at surgery is the most relevant unfavorable prognostic factor. Current guidelines consider the use of adjuvant capecitabine, based on the results of the randomized CREATE-X study, carried out in Asian patients and including a small subset of triple negative tumors. Thus far, evidence on Caucasian patients is limited, and no real-world data are available. Methods: We carried out a multicenter, observational study, involving 44 oncologic centres. Triple negative breast cancer patients with residual disease, treated with adjuvant capecitabine from January 2017 through June 2021, were recruited. We primarily focused on treatment tolerability, with toxicity being reported as potential cause of treatment discontinuation. Secondarily, we assessed effectiveness in the overall study population and in a subset having a minimum follow-up of 2 years. Results: Overall, 270 patients were retrospectively identified. The 50.4% of the patients had residual node positive disease, 7.8% and 81.9% had large or G3 residual tumor, respectively, and 80.4% a Ki-67 >20%. Toxicity-related treatment discontinuation was observed only in 10.4% of the patients. In the whole population, at a median follow-up of 15 months, 2-year disease-free survival was 62%, 2 and 3-year overall survival 84.0% and 76.2%, respectively. In 129 patients with a median follow-up of 25 months, 2-year disease-free survival was 43.4%, 2 and 3-year overall survival 78.0% and 70.8%, respectively. Six or more cycles of capecitabine were associated with more favourable outcomes compared with less than six cycles. Conclusion: The CaRe study shows an unexpectedly good tolerance of adjuvant capecitabine in a real-world setting, although effectiveness appears to be lower than that observed in the CREATE-X study. Methodological differences between the two studies impose significant limits to comparability concerning effectiveness, and strongly invite further research

The satisfactory growth and development at 2 years of age of the INTERGROWTH-21st Fetal Growth Standards cohort support its appropriateness for constructing international standards.

BACKGROUND: The World Health Organization recommends that human growth should be monitored with the use of international standards. However, in obstetric practice, we continue to monitor fetal growth using numerous local charts or equations that are based on different populations for each body structure. Consistent with World Health Organization recommendations, the INTERGROWTH-21st Project has produced the first set of international standards to date pregnancies; to monitor fetal growth, estimated fetal weight, Doppler measures, and brain structures; to measure uterine growth, maternal nutrition, newborn infant size, and body composition; and to assess the postnatal growth of preterm babies. All these standards are based on the same healthy pregnancy cohort. Recognizing the importance of demonstrating that, postnatally, this cohort still adhered to the World Health Organization prescriptive approach, we followed their growth and development to the key milestone of 2 years of age. OBJECTIVE: The purpose of this study was to determine whether the babies in the INTERGROWTH-21st Project maintained optimal growth and development in childhood. STUDY DESIGN: In the Infant Follow-up Study of the INTERGROWTH-21st Project, we evaluated postnatal growth, nutrition, morbidity, and motor development up to 2 years of age in the children who contributed data to the construction of the international fetal growth, newborn infant size and body composition at birth, and preterm postnatal growth standards. Clinical care, feeding practices, anthropometric measures, and assessment of morbidity were standardized across study sites and documented at 1 and 2 years of age. Weight, length, and head circumference age- and sex-specific z-scores and percentiles and motor development milestones were estimated with the use of the World Health Organization Child Growth Standards and World Health Organization milestone distributions, respectively. For the preterm infants, corrected age was used. Variance components analysis was used to estimate the percentage variability among individuals within a study site compared with that among study sites. RESULTS: There were 3711 eligible singleton live births; 3042 children (82%) were evaluated at 2 years of age. There were no substantive differences between the included group and the lost-to-follow up group. Infant mortality rate was 3 per 1000; neonatal mortality rate was 1.6 per 1000. At the 2-year visit, the children included in the INTERGROWTH-21st Fetal Growth Standards were at the 49th percentile for length, 50th percentile for head circumference, and 58th percentile for weight of the World Health Organization Child Growth Standards. Similar results were seen for the preterm subgroup that was included in the INTERGROWTH-21st Preterm Postnatal Growth Standards. The cohort overlapped between the 3rd and 97th percentiles of the World Health Organization motor development milestones. We estimated that the variance among study sites explains only 5.5% of the total variability in the length of the children between birth and 2 years of age, although the variance among individuals within a study site explains 42.9% (ie, 8 times the amount explained by the variation among sites). An increase of 8.9 cm in adult height over mean parental height is estimated to occur in the cohort from low-middle income countries, provided that children continue to have adequate health, environmental, and nutritional conditions. CONCLUSION: The cohort enrolled in the INTERGROWTH-21st standards remained healthy with adequate growth and motor development up to 2 years of age, which supports its appropriateness for the construction of international fetal and preterm postnatal growth standards

Positivity preserving property for a class of biharmonic elliptic problems

The lack of a general maximum principle for biharmonic equations suggests to study under which boundary conditions the positivity preserving property holds. We show that this property holds in general domains for suitable linear combinations of Dirichlet and Navier boundary conditions. The spectrum of this operator exhibits some unexpected features: radial data may generate nonradial solutions. These boundary conditions are also of some interest in semilinear equations, since they enable us to give explicit radial singular solutions to fourth order Gelfand-type problems

Positivity preserving property for a class of biharmonic elliptic problems

The lack of a general maximum principle for biharmonic equations suggests to study under which boundary conditions the positivity preserving property holds.We show that this property holds in general domains for suitable linear combinations of Dirichlet and Navier boundary conditions. The spectrum of this operator exhibits some unexpected features: radial data may generate nonradial solutions. These boundary conditions are also of some interest in semilinear equations, since they enable us to give explicit radial singular solutions to fourth order Gelfand-type problems