A study of second order differential inclusions with four-point integral boundary conditions

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1. [1] A.R. Aftabizadeh, Existence and uniqueness theorems for fourth-order boundary value problems, J. Math. Anal. Appl. 116 (1986), 415-426. doi: 10.1016/S0022-247X(86)80006-3 Zbl0634.34009
2. [2] B. Ahmad, Approximation of solutions of the forced Duffing equation with m-point boundary conditions, Commun. Appl. Anal. 13 (2009) 11-20. Zbl1182.34011
3. [3] B. Ahmad, A. Alsaedi and B. Alghamdi, Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions, Nonlinear Anal. Real World Appl. 9 (2008), 1727-1740. doi: 10.1016/j.nonrwa.2007.05.005 Zbl1154.34311
4. [4] B. Ahmad and S.K. Ntouyas, Existence results for nonlocal boundary value problems for fractional differential inclusions, International Electronic Journal of Pure and Applied Mathematics 1 (2) (2010), 101-114. 
5. [5] B. Ahmad and S.K. Ntouyas, Some existence results for boundary value problems of fractional differential inclusions with non-separated boundary conditions, Electron. J. Qual. Theory Differ. Equ. No. 71 (2010), 1-17. Zbl1206.26005
6. [6] J. Andres, A four-point boundary value problem for the second-order ordinary differential equations, Arch. Math. (Basel) 53 (1989), 384-389. doi: 10.1007/BF01195218 Zbl0667.34024
7. [7] J. Andres, Four-point and asymptotic boundary value problems via a possible modification of Poincaréís mapping, Math. Nachr. 149 (1990), 155-162. doi: 10.1002/mana.19901490112 
8. [8] E.O. Ayoola, Quantum stochastic differential inclusions satisfying a general Lipschitz condition, Dynam. Systems Appl. 17 (2008), 487-502 Zbl1202.81130
9. [9] M. Benaïm, J. Hofbauer, S. Sorin, Stochastic approximations and differential inclusions II. Applications, Math. Oper. Res. 31 (2006), 673-695. doi: 10.1287/moor.1060.0213 Zbl1284.62511
10. [10] A.V. Bicadze and A.A. Samarskii, Some elementary generalizations of linear elliptic boundary value problems (Russian), Anal. Dokl. Akad. Nauk SSSR 185 (1969), 739-740. 
11. [11] A. Boucherif, Second-order boundary value problems with integral boundary conditions, Nonlinear Anal. 70 (2009), 364-371. doi: 10.1016/j.na.2007.12.007 Zbl1169.34310
12. [12] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86. Zbl0677.54013
13. [13] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. Zbl0346.46038
14. [14] Y.-K. Chang, W.T. Li and J.J. Nieto, Controllability of evolution differential inclusions in Banach spaces, Nonlinear Anal. 67 (2007), 623-632. doi: 10.1016/j.na.2006.06.018 
15. [15] H. Covitz and S.B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11. doi: 10.1007/BF02771543 Zbl0192.59802
16. [16] K. Deimling, Multivalued Differential Equations, Walter De Gruyter, Berlin-New York, 1992. doi: 10.1515/9783110874228 Zbl0760.34002
17. [17] P.W. Eloe and B. Ahmad, Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions, Appl. Math. Lett. 18 (2005), 521-527. doi: 10.1016/j.aml.2004.05.009 Zbl1074.34022
18. [18] A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2005. Zbl1025.47002
19. [19] J.R. Graef and J.R.L. Webb, Third order boundary value problems with nonlocal boundary conditions, Nonlinear Anal. 71 (2009), 1542-1551. doi: 10.1016/j.na.2008.12.047 Zbl1189.34034
20. [20] M. Greguš, F. Neumann and F.M. Arscott, Three-point boundary value problems in differential equations, Proc. London Math. Soc. 3 (1964), 459-470. 
21. [21] C.P. Gupta, A second order m-point boundary value problem at resonance, Nonlinear Anal. 24 (1995), 1483-1489. doi: 10.1016/0362-546X(94)00204-U 
22. [22] C.P. Gupta, Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equations, J. Math. Anal. Appl. 168 (1998), 540-551. doi: 10.1016/0022-247X(92)90179-H 
23. [23] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Theory I, Kluwer, Dordrecht, 1997. 
24. [24] V.A. Il'in and E.I. Moiseev, Nonlocal boundary-value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, Diff. Equ. 23 (1987), 803-810. 
25. [25] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer, Dordrecht, The Netherlands, 1991. 
26. [26] A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786. Zbl0151.10703
27. [27] R. Ma, Multiple positive solutions for nonlinear m-point boundary value problems, Appl. Math. Comput. 148 (2004), 249-262. doi: 10.1016/S0096-3003(02)00843-3 Zbl1046.34030
28. [28] S.K. Ntouyas, Nonlocal Initial and Boundary Value Problems: A survey, Handbook on Differential Equations: Ordinary Differential Equations, Edited by A. Canada, P. Drabek and A. Fonda, Elsevier Science B.V., (2005), 459-555. 
29. [29] S.K. Ntouyas, Neumann boundary value problems for impulsive differential inclusions, Electron. J. Qual. Theory Differ. Equ. 2009, Special Edition I, No. 22, pp.~13. Zbl1195.34041
30. [30] M. Pei and S.K. Chang, A quasilinearization method for second-order four-point boundary value problems, Appl. Math. Comput. 202 (2008), 54-66. doi: 10.1016/j.amc.2008.01.026 Zbl1161.65059
31. [31] G.V. Smirnov, Introduction to the theory of differential inclusions, American Mathematical Society, Providence, RI, 2002. Zbl0992.34001
32. [32] Y. Sun, L. Liu, J. Zhang and R.P. Agarwal, Positive solutions of singular three-point boundary value problems for second-order differential equations, J. Comput. Appl. Math. 230 (2009), 738-750. doi: 10.1016/j.cam.2009.01.003 Zbl1173.34016
33. [33] J. Tariboon and T. Sittiwirattham, Positive solutions of a nonlinear three-point integral boundary value problem, Bound. Valur Probl., to appear. 
34. [34] L. Wang, M. Pei and W. Ge, Existence and approximation of solutions for nonlinear second-order four-point boundary value problems, Math. Comput. Modelling 50 (2009), 1348-1359. doi: 10.1016/j.mcm.2008.11.018 Zbl1185.34022
35. [35] J.R.L. Webb and G. Infante, Positive solutions of nonlocal boundary value problems: A unified approach, J. London Math. Soc. 74 (2006), 673-693. doi: 10.1112/S0024610706023179 Zbl1115.34028