T. Chantladze, N. Kandelaki, A. Lomtatidze, and D. Ugulava
The present investigation is stimulated by the works ,  and  in which the authors study oscillatory properties of half-linear ordinary differential equations, of the so-called $P$-Laplacian. Here we consider its two-dimensional version. Moreover, it turns out that the fundamentals of the $P$-Laplacian theory can be successfully involved in a more general scheme which we call the theory of connected pairs. We will see that it contains, on the one hand, the notion of analyticity and, on the other hand, it allows one to apply a very important transformation of the analysis, the Legendre transformation to the investigation of the $P$-Laplacian.
Mathematics Subject Classification: 34K15, 34K40.
Key words and phrases: Half-linear ordinary differential equations, the P-Laplacian, connected pairs.