In the present project there will be studied qualitative properties of the half-linear differential equation (r(t)fí(y´))´ +p(t)fí(y)=0, where fí(x) = lx]alfa-2x and a > 1, its discrete counterpart - half-linear difference equation, and other related equ ations. It is a well-known fact that there exists a striking similarity between theories of (HLDE) and Sturm-Liouville differential equation (which is the special case of (HLDE) for alfa = 2) that enable to use methods known from theory of linear equatio ns for investigating of (HLDE) and hereby to obtain the strong results. The study of (HLDE) is important (among others) for the following reasons: 1) Equation (HLDE) is a special (one-dimensional) case of partial differential equation with the so-called alfa-Laplacian which describes many physical and chemical phenomena. The results obtained in the connection with equation (HLDE) are good bases for an extension to the multidimensional case, 2) We can use the results concerning (HLDE) in the study of equ

Publications