Second order boundary value problems of nonsingular type on time scales

Document Type : Research Paper

Authors

Department of Mathematics, Ege University, 35100 Bornova, Izmir, Turkey.

Abstract

In this study, the existence of positive solutions is considered for second-order boundary value problems on any time scales even in the case when y ≡ 0 may also be a solution.

Keywords


  • [1]          R. P. Agarwal and D. O’Regan, Second and Higher Order Boundary Value Problems of Non- singular Type, Bull. Belg. Math. Soc., 7 (2000), 43-52.
  • [2]          L. E. Bobisud and D. O’Regan, Existence of Positive Solutions for Singular Ordinary Differ- ential Equations with Nonlinear Boundary Conditions, Proc. Amer. Math. Soc., 124 (1996), 2081-2087.
  • [3]          M. Bohner and A. Petterson, Advances in Dynamic Equations on Time Scales, Birkhauser, (2003), 358.
  • [4]          P. W. Eloe and J. Henderson, Positive Solutions for Higher Order Ordinary Differential equa- tions, Electron J. Differential Equations, 3 (1995), 1-8.
  • [5]          L. H. Erbe and H. Wang, On The Existence of Positive Solutions of Ordinary Differential Equations, Proc. Amer. Math. Soc., 120 (1994), 743-748.
  • [6]          A. M. Fink, J. A. Gatica, and G. E. Hernandez, Eigenvalues of Generalized Gelfand Models, Nonlinear Anal., 20 (1993), 1453-1468.
  • [7]          S. Hilger, Ein Mabkettenkalkul mit Anvendung auf Zentrumsmannigfaltigkeiten, PhD thesis, Universitat Wurzburg(1988).
  • [8]          Xu, Jiafa, O’ Regan, and Donald, Positive Solutions for a Second Order Boundary  Value  Prob- lem on Time Scale, J. Appl. Math. Comput., 51(1-2) (2016), 127-144.
  • [9]          D. O’Regan, Existance Theory for Nonlinear Ordinary Differantial Equations, Kluwer Academic Publishers, Dordrecht, (1997), 1-22.
  • [10]        D. O’Regan, Theory of Singular Boundary Value Problems, World Scientific, Singapore (1994), 168.
  • [11]        P. J. Y. Wong and R. P. Agarwal, On the Existence of Solutions of Singular Boundary Value Problems for Higher Order Difference Equations, Nonlinear Anal., 28 (1997), 277-287.
  • [12]        X. L. Zhang and J. J. Fan, Positive Solutions to a Second Order Non-Linear Boundary Value Problem on Time Scales, Acta Anal. Func. Appl.,14(4) (2012), 370-376.