On the solvability of third-order three point systems of differential equations with dependence on the first derivative

This paper presents sufficient conditions for the solvability of the third order three point boundary value problem \begin{equation*} \left\{ \begin{array}{c} -u^{\prime \prime \prime }(t)=f(t,\,v(t),\,v^{\prime }(t)) \\ -v^{\prime \prime \prime }(t)=h(t,\,u(t),\,u^{\prime }(t)) \\ u(0)=u^{\prime }(0)=0,u^{\prime }(1)=\alpha u^{\prime }(\eta ) \\ v(0)=v^{\prime }(0)=0,v^{\prime }(1)=\alpha v^{\prime }(\eta ). \end{array} \right. \end{equation*} The arguments apply Green's function associated to the linear problem and the Guo--Krasnosel'ski\u{\i} theorem of compression-expansion cones. The dependence on the first derivatives is overcome by the construction of an adequate cone and suitable conditions of superlinearity/sublinearity near $0$ and $+\infty .$ Last section contains an example to illustrate the applicability of the theorem.Comment: 21 page

Low-carbon technology for the rising middle class

This policy brief will discuss the role of local and international technology and innovation policies for low-carbon development of the rising middle class in developing countries. Although a large segment of the population of most developing countries remains severely deprived, most developing countries also have a significant and growing part of the population that could be a feasible target for low-carbon policies. In addition to how industrialised countries decide to reduce their emissions, a major determinant of the carbon intensity of the world economy and our collective ability to stay below 2°C global mean temperature rise, is how the rising middle class in developing countries will develop – along a low-carbon or a higher-carbon pathway. If this rising middle class could embark on a lower-carbon consumption pathway, for instance in their electricity use, their transportation demand and modes, their eating habits and other consumption patterns, this could structurally avoid a considerable amount of greenhouse gas emissions and yield other social, environmental and health benefits. As strong carbon policies incentivising such pathways are unlikely to happen soon in developing countries, technology policies can provide a solution, given they can be aimed at consumption patterns of the rising middle class specifically. This paper makes several case-based recommendations that can put those in developing countries that benefit from a more sustainable lifestyle on a low-carbon development path

Nonlinear estimators with integrated regressors but without exogeneity

This paper analyzes nonlinear cointegrating regressions as have been recently analyzed in a paper by Park and Phillips in Econometrica. I analyze the consequences of removing Park and Phillips' exogeneity assumption, which for the special case of a linear model would imply the asymptotic validity of the least squares estimator for linear cointegrating regressions. For the linear model, the unlikeliness of such an exogeneity assumption to hold in practice has inspired the `fully modified' technique, the `leads and lags' technique, and Park's `canonical regressions'. In this paper, a `fully modified' type technique is proposed for nonlinear cointegrating regressions. The mathematical tool for proving this result is a new so-called `convergence to stochastic integrals' result. This result is proven for objects that are summations of a stationary random variable times an asymptotically homogeneous function of an integrated process. The increments of the integrated process are allowed to be correlated with the stationary random variable. This result is derived by extending a line of proof pioneered in work by Chan and Weinonlinearity, integrated process, cointegration, fully modified