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Citation - WoS: 7
Citation - Scopus: 7
Positive Solutions of Nonlinear Multi-Point Boundary Value Problems
(Springer, 2018-05-17) Dogan, Abdulkadir
This paper deals with the existence of positive solutions of nonlinear differential equation subject to the boundary conditions By using Schauder's fixed point theorem, we show that it has at least one positive solution if f is nonnegative and continuous. Positive solutions of the above boundary value problem satisfy theHarnack inequality inf(0 <= t <= 1) u(t) >= gamma parallel to u parallel to(infinity.)
Citation - Scopus: 1
On the Existence of Positive Solutions for the Time-Scale Dynamic Equations on Infinite Intervals
(Springer, 2020) Doǧan, Abdülkadir Muhittin
This paper investigates the existence of positive solutions to time-scale boundary value problems on infinite intervals. By applying the Leggett-Williams fixed point theorem in a cone, some new results for the existence of at least three positive solutions of boundary value problems are found. With infinite intervals, the theorem can be used to prove the existence of solutions of boundary value problems for nonlinear dynamic equations dependence on the delta derivative explicitly. Our results are new for the special cases of difference equations and differential equations as well as in the general time scale setting. © 2020 Elsevier B.V., All rights reserved.

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