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Öğe A New Theorem on The Existence of Positive Solutions of Singular Initial-Value Problem for Second Order Differential Equations(Emrah Evren KARA, 2019) Aslanov, AfganWe proved a new theorem on the existence of positive solutions to initial-value problems for second-order nonlinear singular differential equations. The existence of solutions is proven under considerably weaker than previously known conditions.Öğe A Note on The Asymptotic Solution of Second Order Nonlinear Differential Equation(Springer Basel Ag, 2022) Aslanov, AfganWe study the existence of solutions of second-order nonlinear differential equations. It is shown that the second-order nonlinear differential equation x '' = f (t, x, x') has a positive (and so non-oscillatory) solution asymptotic to the function phi(t) = t at infinity and satisfies the initial condition x(0) = 0.Öğe On the asymptotic behavior of positive solutions to nonlinear second-order differential equations(Springer Wien, 2022) Aslanov, AfganWe study the existence of solutions of second-order nonlinear differential equations on half-line. It is shown that the second-order nonlinear differential equation x '' = f (t, x) has a positive solution asymptotic to the function phi(t) = t at infinity and satisfies the initial condition x(0) = 0. Existence of solutions is proven under conditions which are considerably weaker than previously known conditions. An application to semilinear Schrodinger equations is also presented.Öğe Positive solutions of semilinear schrodinger equations in two-dimensional exterior domains(Springer Wien, 2023) Aslanov, AfganWe consider the existence of a positive (generally unbounded) solution to the semilinear Schrodinger equation in a two-dimensional exterior domain. Our method relies on the comparison method, that is, the technique of super/sub-solutions. An application to Emden-Fowler equation is also presented.Öğe The Existence of Positive Solutions of Singular Initial-Value Problem for Second Order Differential Equations-2(Emrah Evren KARA, 2020) Aslanov, AfganWe consider the singular initial value problem for the second order differential equation. We interested in the existence of positive solutions and proved an easily applicable theorem on the existence of positive solutions to initial-value problems for second-order nonlinear singular differential equations. The previously established result on the existence of positive solution by Agarwal and O'Regan is not easy for the applications due to very complex definition of a new function and their properties in the statement of their theorem. We used the Lebesgue dominated convergence theorem and the Schauder--Tychonoff theorem in the proof of the main result. The main result can be easily applied for the singular and regular type of problems.
