On asymptotic behavior of solutions of functional-differential and discrete equations
The project N 31/09 “On asymptotic behavior of solutions of functional-differential and discrete equations” by the professor of Iv. Javakhishvili Tbilisi State University Roman Koplatadze won the 2012 year competitions in fundamental grant. The purpose of the grant was to create the new study methods for asymptotic behavior of solutions of differential and discrete equations. The new results was found about existing of vanished, oscillated, and unbounded solutions of functional differential equations. It was investigated essential nonlinear and almost linear differential equations, generalized of Emden-Fowler nonlinear and linear differential equations. This type of equations were learned as first time. Furthermore, problems about oscillation of solutions of discrete equations were learned, where optimal results are obtained. These results are the generalize of the before well known results, which were published in 5 international (Impact Factor) and 3 reviewed scientific journals.
- "On asymptotic behavior of solutions of generalized Enmden-Fowler differential equations with delay argument". 2014, Art. ID 168425, 13pp. Abstract and Applied Analysis Hindawi Publishing Corporation, R. Koplatadze, A. Domoshnitski.
- " Oscillation criteria for first order linear difference equations with several delay arguments”. 17 (2014), no. 2, 248-267. Nonlinear Oscillations, Springer, R. Koplatadze, S. pinelas.
- "Oscillation criteria for differential equations with several non-monotone arguments”. 53 (2015), no. 3, 14pp. Funkcialaj Ekvacioj Japan Publications Trading Go. Ltd. R. Koplaradze, J. Infante, I. Stavroulakis.
- "The specific properties of solutions of first order differential equations with several delay arguments”. 50 (2015), no. 5, 229-235. Journal of Contemporary Mathematical Analysis Springer, .R. Koplatadze.
- "On higner order generalized Emden-Fowler differential equations with delay arguments". 18 (2015), no. 4, 507-526. Nonlinear Oscillations, Springer, R. Koplatadze, A. Domoshnitski.
- ”On oscillatory properties of solutions of n-th order generalized Emden-Fowler differential equations with delay argument”. 40 (2014), 32-38, Reports of Seminar of I. Vekua Institute of Applied Mathematics R. Koplatadze.
- ”Oscillation criteria for difference equations with severaldelay arguments”. 40 (2014), 28-31, Reports of Seminar of I. Vekua Institute of Applied Mathematics, R. Koplatadze.
- ”Oscillation criteria for differential and discrete equations with several delays”. 18 (2014), 3-10, Bulletin of TICMI, R. koplatadze.