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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 708734, 7 pages
Existence Results for Solutions of Integral Boundary Value Problems on Time Scales
Department of Mathematics, Ege University, Bornova, 35100 Izmir, Turkey
Received 27 November 2012; Accepted 12 March 2013
Academic Editor: Xinan Hao
Copyright © 2013 Erbil Cetin and F. Serap Topal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- S. Hilger, “Analysis on measure chains—a unified approach to continuous and discrete calculus,” Results in Mathematics, vol. 18, no. 1-2, pp. 18–56, 1990.
- M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001.
- M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, Mass, USA, 2003.
- F. A. Davidson and B. P. Rynne, “The formulation of second-order boundary value problems on time scales,” Advances in Difference Equations, vol. 2006, Article ID 31430, 10 pages, 2006.
- L. Erbe and A. Peterson, “Green's functions and comparison theorems for differential equations on measure chains,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 6, no. 1, pp. 121–137, 1999.
- R. A. Khan, “The generalized method of quasilinearization and nonlinear boundary value problems with integral boundary conditions,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 10, pp. 1–9, 2003.
- Z. Yang, “Existence and nonexistence results for positive solutions of an integral boundary value problem,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 8, pp. 1489–1511, 2006.
- B. Ahmad, A. Alsaedi, and B. S. Alghamdi, “Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions,” Nonlinear Analysis: Real World Applications, vol. 9, no. 4, pp. 1727–1740, 2008.
- F. M. Atici and G. Sh. Guseinov, “On Green's functions and positive solutions for boundary value problems on time scales,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 75–99, 2002.
- G. W. Batten Jr., “Second-order correct boundary conditions for the numerical solution of the mixed boundary problem for parabolic equations,” Mathematics of Computation, vol. 17, pp. 405–413, 1963.
- J. R. Cannon, S. P. Esteva, and J. van der Hoek, “A Galerkin procedure for the diffusion equation subject to the specification of mass,” SIAM Journal on Numerical Analysis, vol. 24, no. 3, pp. 499–515, 1987.
- L. I. Kamynin, “A boundary value problem in the theory of heat conduction with boundary condition,” USSR Computational Mathematics and Mathematical Physics, vol. 4, no. 6, pp. 33–59, 1964.
- A. Bouziani and N.-E. Benouar, “Mixed problem with integral conditions for a third order parabolic equation,” Kobe Journal of Mathematics, vol. 15, no. 1, pp. 47–58, 1998.
- M. Denche and A. L. Marhoune, “Mixed problem with integral boundary condition for a high order mixed type partial differential equation,” Journal of Applied Mathematics and Stochastic Analysis, vol. 16, no. 1, pp. 69–79, 2003.
- J. M. Gallardo, “Second-order differential operators with integral boundary conditions and generation of analytic semigroups,” The Rocky Mountain Journal of Mathematics, vol. 30, no. 4, pp. 1265–1292, 2000.
- T. Jankowski, “Differential equations with integral boundary conditions,” Journal of Computational and Applied Mathematics, vol. 147, no. 1, pp. 1–8, 2002.
- A. V. Kartynnik, “A three-point mixed problem with an integral condition with respect to the space variable for second-order parabolic equations,” Differential Equations, vol. 26, no. 9, pp. 1160–1166, 1990.
- L. Liu, X. Hao, and Y. Wu, “Positive solutions for singular second order differential equations with integral boundary conditions,” Mathematical and Computer Modelling, vol. 57, no. 3-4, pp. 836–847, 2013.
- X. Zhang and W. Ge, “Symmetric positive solutions of boundary value problems with integral boundary conditions,” Applied Mathematics and Computation, vol. 219, no. 8, pp. 3553–3564, 2012.
- S. A. Brykalov, “A second-order nonlinear problem with two-point and integral boundary conditions,” Georgian Mathematical Journal, vol. 1, no. 3, pp. 243–249, 1994.
- M. A. Krasnosel'skii, Positive Solutions of Operator Equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1964.