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Newsletter
Project Name :
Nonlinear Boundary Value Problems and Their Applications to the Qualitative Theory of Differential Equations
Donor Organization :
Shota Rustaveli National Science Foundation
Budget:
150 000 GEL
Grant number :
FR/317/5-101/12
Direction :
5 Mathematics, Mechanics
Subdirection :
5-101 Differential Equations
Key word :
Differential equation; boundary value problem
Description :
The goal of the proposed project is to construct a theory of nonlinear boundary value problems for ordinary differential and functional differential equations and systems.
In the framework of the project, a unified method for investigation of the above-mentioned problems will be elaborated which means the reduction of the question on the solvability of those problems to the uniform a priori estimates of solutions of analogous problems for one-parameter families of differential equations and systems. This method will be based on new a priori estimates of solutions of one-sided differential inequalities and systems of such inequalities under various nonlinear boundary conditions.
Using this method, optimal in a certain sense conditions will be established guaranteeing the solvability in a finite and an infinite interval, respectively, of nonlinear boundary value problems for:
a) second and higher order differential equations and systems with singularities with respect to time and phase variables;
b) higher order singular functional differential equations and systems.
These results will be applied to the investigation of the existence problem of so-called proper solutions (i.e., nontrivial solutions, defined in an infinite interval) of nonlinear differential equations and systems. Namely, for higher order nonautonomous differential equations and systems with rapidly growing with respect to phase variables right-hand sides, sufficient conditions for the existence of proper oscillatory and monotone solutions will be found. Analogous results will be obtained for strongly nonlinear functional differential equations and systems.
Duration :
15/04/2013 - 14/04/2016
Leader :
Ivan Kiguradze
Project manager :
Project participant(s) :
Nino Partsvania
15/04/2013 - 14/04/2016
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