Semiclassical analysis for pseudo-relativistic Hartree equations

In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation $\sqrt{-\varepsilon^2 \Delta + m^2}u + V u = (I_\alpha * |u|^{p}) |u|^{p-2}u$ in $\mathbb{R}^N$ where $m>0$, $2 \leq p < \frac{2N}{N-1}$, $V \colon \mathbb{R}^N \to \mathbb{R}$ is an external scalar potential, $I_\alpha (x) = \frac{c_{N,\alpha}}{|x|^{N-\alpha}}$ is a convolution kernel, $c_{N,\alpha}$ is a positive constant and $(N-1)p-N<\alpha <N$. For $N=3$, $\alpha=p=2$, our equation becomes the pseudo-relativistic Hartree equation with Coulomb kernel.Comment: Accepted for publication by Journal of Differential Equation

Ground states for the pseudo-relativistic Hartree equation with external potential

We prove existence of positive ground state solutions to the pseudo-relativistic Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{l} \sqrt{-\Delta +m^2} u +Vu = \left( W * |u|^{\theta} \right)|u|^{\theta -2} u \quad\text{in $\mathbb{R}^N$}\\ u \in H^{1/2}(\mathbb{R}^N) \end{array} \right. \end{equation*} where $N \geq 3$, $m >0$, $V$ is a bounded external scalar potential and $W$ is a convolution potential, radially symmetric, satisfying suitable assumptions. We also furnish some asymptotic decay estimates of the found solutions.Comment: In pres

Multi-peak solutions for magnetic NLS equations without non--degeneracy conditions

In the work we consider the magnetic NLS equation (\frac{\hbar}{i} \nabla -A(x))^2 u + V(x)u - f(|u|^2)u = 0 \quad {in} \R^N where $N \geq 3$, $A \colon \R^N \to \R^N$ is a magnetic potential, possibly unbounded, $V \colon \R^N \to \R$ is a multi-well electric potential, which can vanish somewhere, $f$ is a subcritical nonlinear term. We prove the existence of a semiclassical multi-peak solution u\colon \R^N \to \C, under conditions on the nonlinearity which are nearly optimal.Comment: Important modification in the last part of the pape

A MODEL OF PESTICIDE RESISTANCE AS A COMMON PROPERTY AND EXHAUSTIBLE RESOURCE

A dynamic farm production model analyzes the interaction between the externalities caused by pest mobility and the development of pesticide resistance, a nonrenewable resource, in the context of agricultural biotechnologies. The model measures the effect of farmers' myopic behavior and the impact of pest mobility on the path of resistance.biotechnology, common property resource, European Corn Borer, externalities, pesticide resistance, intertemporal optimization, Research and Development/Tech Change/Emerging Technologies,

OPTIMAL PESTICIDE USAGE WITH RESISTANCE AND ENDOGENOUS TECHNOLOGICAL CHANGE

This paper develops a model analyzing the first best policy for a social planner when pesticide use causes resistance, the level of pest infestation is heterogeneous among farmers, and the development of a backstop technology is an endogenous and uncertain process which depends on the cumulative amount of R&D effort.Crop Production/Industries,

MANAGING PEST RESISTANCE: THE POTENTIAL OF CROP ROTATIONS AND SHREDDING

The current debate over resistance management plans mandated by the Environmental Protection Agency for transgenic crops ignores management practices that are complementary to refuge schemes. A dynamic production model is developed that measures the costs and benefits of crop rotation and shredding in terms of delaying resistance to Bt corn.biotechnology, common property resource, crop rotation, European Corn Borer, externalities, insecticide resistance, integrated pest management, intertemporal optimization, Crop Production/Industries, Research and Development/Tech Change/Emerging Technologies,

Economic issues in resistance management

This dissertation analyzes economic issues related to the use of agricultural pesticides and antibiotics. The efficacy of both these chemical compounds depends on the existence of susceptible targets. However, through natural selection, their utilization increases the frequency of the genes resistant to the pesticide or drug in the target population, and it decreases the available biological capital of genetic susceptibility, increasing resistance;The aim of this dissertation is to analyze the characteristics of optimal resistance management strategies. An empirical analysis is offered in case of bioengineered Bt corn, which underlines the importance of pest mobility, and the externalities it causes, in the development of resistance;Chapter II consists of a general theoretical model on resistance development that incorporates a spatial dimension. This allows the analysis of the impact of pest mobility on the effectiveness of refuges, areas in which the pesticides are not used to preserve the existence of susceptible pests. A discussion of eradication policies and of the role of cross-resistance is included;Chapter III presents an empirical analysis of the role of pest mobility in the development of resistance in the case of Bt corn. The model includes the existence of mandatory (structured) refuges for farmers planting Bt crops and analyzes the impact of incomplete market penetration on resistance development and profits. If part of the crop production area is seeded with non-bioengineered seed, these fields act as an unstructured refuge. The current policy is effectively based on a 100% market penetration. This is not necessarily a realistic assumption. We explicitly evaluate the role of market penetration on resistance;Chapter IV concentrates on the optimal use of existing antibiotics and on the optimal time path of investment in the development of new technologies. The intertemporal allocation of susceptibility and the development of alternative technologies are important social issues, particularly in the case of antibiotics, because health can be considered a necessary good. The analysis focuses on the role of endogenous technological and the investment of resources in alternative technologies;Lastly, some general conclusions on the importance of externalities and technological change in the mining of susceptibility are presented

Land-Use Implications of the Changes in Energy Prices

Land Economics/Use, Resource /Energy Economics and Policy,

MANAGING EUROPEAN CORN BORER RESISTANCE TO BT CORN WITH DYNAMIC REFUGES

We develop a dynamic bioeconomic model of temporally optimal dynamic refuge recommendations for resistance management when a backstop technology arrives at a known date. The impact of the characteristics of the backstop on the use of the current technology, and the difference between static and dynamic refuges are examined.Crop Production/Industries,