On a nonlocal asymmetric Kirchhoff problem

This work is devoted to study the existence of nontrivial solutions to nonlocal asymmetric problems involving the [Formula: see text]-Laplacian. [Formula: see text] where [Formula: see text] is a bounded domain with smooth boundary, [Formula: see text] is a Kirchhoff function, [Formula: see text] and [Formula: see text] is of subcritical polynomial or subcritical exponential growth. Moreover, the existence of nontrivial solutions for the above problem is obtained by using variational methods combined with the Moser–Trudinger inequality. Our interest then is to study [Formula: see text] without the analogue of Ambrosetti–Rabinowitz superquadratic condition ([Formula: see text] condition for short) in the positive semi-axis. To the best of our best knowledge, our results are new even in the asymmetric Kirchhoff Laplacian and [Formula: see text]-Laplacian cases.

Wind Forecasts for Rocket and Balloon Launches at the Esrange Space Center Using the WRF Model

High-altitude balloons and rockets are regularly launched at the Esrange Space Center (ESC) in Kiruna, Sweden, with the aim of retrieving atmospheric data for meteorological and space studies in the Arctic region. Meteorological conditions, particularly wind direction and speed, play a critical role in the decision of whether to go ahead with or postpone a planned launch. Given the lack of high-resolution wind forecasts for this remote region, the Weather Research and Forecasting (WRF) Model is used to downscale short-term forecasts given by the Global Forecast System (GFS) for the ESC for six 5-day periods in the warm, cold, and transition seasons. Three planetary boundary layer (PBL) schemes are considered: the local Mellor–Yamada–Janjić (MYJ), the nonlocal Yonsei University (YSU), and the hybrid local–nonlocal Asymmetric Convective Model 2 (ACM2). The ACM2 scheme is found to provide the most skillful forecasts. An analysis of the WRF Model output against the launch criteria for two of the most commonly launched vehicles, the sounding rockets Veículo de Sondagem Booster-30 (VSB-30) and Improved Orion, reveals probability of detection (POD) values that always exceeds 60% with the false alarm rate (FAR) generally below 50%. It is concluded that the WRF Model, in its present configuration, can be used to generate useful 5-day wind forecasts for the launches of these two rockets. The conclusions reached here are applicable to similar sites in the Arctic and Antarctic regions.