No abstract

LetLdenote the operator generated inL2(R+)by Sturm-Liouville equation−y′′+q(x)y=λ2y,x∈R+=[0,∞),y′(0)/y(0)=α0+α1λ+α2λ2, whereqis a complex-valued function andαi∈ℂ,i=0,1,2withα2≠0. In this article, we investigate the eigenvalues and the spectral singularities ofLand obtain analogs of Naimark and Pavlov conditions forL.

In this study, a methodology was suggested for wind and solar energy investment plans through linear optimization model for the countries with an energy-based current deficit problem. The originality of the study is that it is a renewable energy investment model based on the functioning of the balance of payments for current deficit reduction, which has not previously been encountered in the literature. While creating the model, without causing external economic imbalance, certain parameters were taken into consideration such as profit transfers for the foreign direct investments, interest payments for the domestic investments, import rates for the wind and solar energy systems, energy electric power production values, electric power load balance, electricity transmission infrastructure, CO 2 emission, future electric power demand projection, and import source rates in the electric power production. It was proven that the model, for the 2019-2030 period in Turkey, not only is an opportunity for decreasing the current deficit but also ensures reaching the CO 2 emission reduction target. Additionally, through the investments in wind and solar energy, it was calculated that fossil-based electric power production will decrease by 80%, and a CO 2 reduction will be provided, which is equivalent of 100 million tonnes GWh natural gas. As a more general result, an optimization model was created which provides a solution for countries coping with energy-based current deficit in economic terms, energy-based air pollution in environmental terms, and renewable energy technology insufficiency.

Through using a linear optimization model that interprets solar energy and current deficit parameters, investment plans were performed for countries which have current deficit problem of energy source. The specifics of the study are due to the linear optimization model, which reveals the current deficit and solar energy together for the investment strategy. While the model is constituted, without affecting the existed current account, some parameters based on such as profit transfers for foreign investments, payments of interest for domestic investments, import rates for photovoltaic solar panels, solar energy electricity production values, electricity demand projection for the future and import resource rates for electricity production. In the framework of these constraints of the model, the effects of solar systems on domestic investment and foreign direct investments on current account balance are analyzed for the period of 2017–2030 in Turkey. In the application of the model in Turkey to reduce the current deficit, this is concluded that the solar energy is a significant opportunity. In addition, the linear optimization model is considered as a reference for countries facing energy-related current deficit problems.

We consider the operator generated in by the differential expression , and the boundary condition , where is a complex-valued function and , with . In this paper we obtain the properties of the principal functions corresponding to the spectral singularities of .