Howard and Maric have recently developed nice nonoscillation theorems for the differential equation U" + q(t)y = 0 (*) by means of regularly varying functions in the sense of Karamata. The purpose of this paper is to show that their results can be fully generalized to differential equations of the form, (p(t)y?)? + q(t)y = o (**) by using the notion of generalized Karamata functions, which is needed to comprehend how delicately the asymptotic behavior of solutions of (**) is affected by the function p(t).

Predicting the risk of financial distress of enterprises is an inseparable part of financial-economic analysis, helping investors and creditors reveal the performance stability of any enterprise. The acceptance of national conditions, proper use of financial predictors and statistical methods enable achieving relevant results and predicting the future development of enterprises as accurately as possible. The aim of the paper is to compare models developed by using three different methods (logistic regression, random forest and neural network models) in order to identify a model with the highest predictive accuracy of financial distress when it comes to industrial enterprises operating in the specific Slovak environment. The results indicate that all models demonstrated high discrimination accuracy and similar performance; neural network models yielded better results measured by all performance characteristics. The outputs of the comparison may contribute to the development of a reputable prediction model for industrial enterprises, which has not been developed yet in the country, which is one of the world’s largest car producers.

The risk of corporate financial distress negatively affects the operation of the enterprise itself and can change the financial performance of all other partners that come into close or wider contact. To identify these risks, business entities use early warning systems, prediction models, which help identify the level of corporate financial health. Despite the fact that the relevant financial analyses and financial health predictions are crucial to mitigate or eliminate the potential risks of bankruptcy, the modeling of financial health in emerging countries is mostly based on models which were developed in different economic sectors and countries. However, several prediction models have been introduced in emerging countries (also in Slovakia) in the last few years. Thus, the main purpose of the paper is to verify the predictive ability of the bankruptcy models formed in conditions of the Slovak economy in the sector of agriculture. To compare their predictive accuracy the confusion matrix (cross tables) and the receiver operating characteristic curve are used, which allow more detailed analysis than the mere proportion of correct classifications (predictive accuracy). The results indicate that the models developed in the specific economic sector highly outperform the prediction ability of other models either developed in the same country or abroad, usage of which is then questionable considering the issue of prediction accuracy. The research findings confirm that the highest predictive ability of the bankruptcy prediction models is achieved provided that they are used in the same economic conditions and industrial sector in which they were primarily developed.

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