43 research outputs found
The Nehari manifold approach for -Laplacian problem with Neumann boundary condition
In this paper, we consider the system
\begin{eqnarray*}
\left\{\begin{array}{ll}
-\Delta_{p(x)} u + |u|^{p(x)-2}u = \lambda a(x)|u|^{r_1(x)-2}u + \frac{\alpha(x)}{\alpha(x) + \beta(x)} c(x)|u|^{\alpha(x)-2}u|v|^{\beta(x)} &~\textrm{in}~\Omega\\
-\Delta_{q(x)} v+|v|^{q(x)-2}v = \mu b(x)|v|^{r_2(x)-2}v + \frac{\beta(x)}{\alpha(x) + \beta(x)} c(x)|v|^{\beta(x)-2}v|u|^{\alpha(x)} & ~\textrm{in}~\Omega\\
\frac{\partial u}{\partial \gamma} = \frac{\partial v}{\partial \gamma}= 0 & \textrm{on}~ \partial \Omega
\end{array}\right.
\end{eqnarray*}
where is a bounded domain with smooth boundary and is the outer unit normal to . Under suitable assumptions, we prove the existence of positive solutions by using the Nehari manifold and some variational techniques
On a class of nonuniformly nonlinear systems with Dirichlet boundary conditions
The existence and multiplicity of weak solutions for some nonuniformly nonlinear elliptic systems are obtained by using the minimum principle and the Mountain-pass theorem.Існування та кратність слабких розв'язків деяких нерівномірно нєлінійних еліптичних систем досліджено за допомогою принципу мінімуму та теореми про гірський перевал
Global, regional, and national age-sex-specific mortality and life expectancy, 1950–2017: a systematic analysis for the Global Burden of Disease Study 2017
BACKGROUND:
Assessments of age-specific mortality and life expectancy have been done by the UN Population Division, Department of Economics and Social Affairs (UNPOP), the United States Census Bureau, WHO, and as part of previous iterations of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD). Previous iterations of the GBD used population estimates from UNPOP, which were not derived in a way that was internally consistent with the estimates of the numbers of deaths in the GBD. The present iteration of the GBD, GBD 2017, improves on previous assessments and provides timely estimates of the mortality experience of populations globally.
METHODS:
The GBD uses all available data to produce estimates of mortality rates between 1950 and 2017 for 23 age groups, both sexes, and 918 locations, including 195 countries and territories and subnational locations for 16 countries. Data used include vital registration systems, sample registration systems, household surveys (complete birth histories, summary birth histories, sibling histories), censuses (summary birth histories, household deaths), and Demographic Surveillance Sites. In total, this analysis used 8259 data sources. Estimates of the probability of death between birth and the age of 5 years and between ages 15 and 60 years are generated and then input into a model life table system to produce complete life tables for all locations and years. Fatal discontinuities and mortality due to HIV/AIDS are analysed separately and then incorporated into the estimation. We analyse the relationship between age-specific mortality and development status using the Socio-demographic Index, a composite measure based on fertility under the age of 25 years, education, and income. There are four main methodological improvements in GBD 2017 compared with GBD 2016: 622 additional data sources have been incorporated; new estimates of population, generated by the GBD study, are used; statistical methods used in different components of the analysis have been further standardised and improved; and the analysis has been extended backwards in time by two decades to start in 1950.
FINDINGS:
Globally, 18·7% (95% uncertainty interval 18·4–19·0) of deaths were registered in 1950 and that proportion has been steadily increasing since, with 58·8% (58·2–59·3) of all deaths being registered in 2015. At the global level, between 1950 and 2017, life expectancy increased from 48·1 years (46·5–49·6) to 70·5 years (70·1–70·8) for men and from 52·9 years (51·7–54·0) to 75·6 years (75·3–75·9) for women. Despite this overall progress, there remains substantial variation in life expectancy at birth in 2017, which ranges from 49·1 years (46·5–51·7) for men in the Central African Republic to 87·6 years (86·9–88·1) among women in Singapore. The greatest progress across age groups was for children younger than 5 years; under-5 mortality dropped from 216·0 deaths (196·3–238·1) per 1000 livebirths in 1950 to 38·9 deaths (35·6–42·83) per 1000 livebirths in 2017, with huge reductions across countries. Nevertheless, there were still 5·4 million (5·2–5·6) deaths among children younger than 5 years in the world in 2017. Progress has been less pronounced and more variable for adults, especially for adult males, who had stagnant or increasing mortality rates in several countries. The gap between male and female life expectancy between 1950 and 2017, while relatively stable at the global level, shows distinctive patterns across super-regions and has consistently been the largest in central Europe, eastern Europe, and central Asia, and smallest in south Asia. Performance was also variable across countries and time in observed mortality rates compared with those expected on the basis of development.
INTERPRETATION:
This analysis of age-sex-specific mortality shows that there are remarkably complex patterns in population mortality across countries. The findings of this study highlight global successes, such as the large decline in under-5 mortality, which reflects significant local, national, and global commitment and investment over several decades. However, they also bring attention to mortality patterns that are a cause for concern, particularly among adult men and, to a lesser extent, women, whose mortality rates have stagnated in many countries over the time period of this study, and in some cases are increasing
Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017
A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4 (62.3 (55.1�70.8) million) to 6.4 (58.3 (47.6�70.7) million), but is predicted to remain above the World Health Organization�s Global Nutrition Target of <5 in over half of LMICs by 2025. Prevalence of overweight increased from 5.2 (30 (22.8�38.5) million) in 2000 to 6.0 (55.5 (44.8�67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic. © 2020, The Author(s)
Author Correction: Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017 (Nature Medicine, (2020), 26, 5, (750-759), 10.1038/s41591-020-0807-6)
An amendment to this paper has been published and can be accessed via a link at the top of the paper. © 2020, The Author(s)
Author Correction: Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017 (Nature Medicine, (2020), 26, 5, (750-759), 10.1038/s41591-020-0807-6)
An amendment to this paper has been published and can be accessed via a link at the top of the paper. © 2020, The Author(s)
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A remark on the existence of positive solutions for variable exponent elliptic systems
AbstractIn this article, we consider the system of differential equations-Δp(x)u=λp(x)[a(x)uα(x)vγ(x)+h1(x)]inΩ,-Δq(x)v=λq(x)[b(x)uδ(x)vβ(x)+h2(x)]inΩ,u=v=0on∂Ω,where Ω⊂RN is a bounded domain with C2-boundary ∂Ω,1<p(x),q(x)∈C1(Ω¯) are functions. The operator −Δp(x) u=−div(∣∇u∣p(x)−2∇u) is called the p(x)-Laplacian. When α, β, δ, γ satisfy some suitable conditions, we prove the existence of positive solution via sub-supersolution arguments without assuming sign conditions on the functions h1 and h2