Systems of differential inclusions in the absence of maximum principles and growth conditions

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1. [1] J. Andres and L. Górniewicz, Topological fixed point principles for boundary value problems. Topological Fixed Point Theory and Its Applications, 1, Kluwer Academic Publishers, Dordrecht 2003. Zbl1029.55002
2. [2] A. Arara, M. Benchohra, S.K. Ntouyas and A. Ouahab, Existence results for boundary value problems for fourth-order differential inclusions with nonconvex valued right hand side, Arch. Math. (Brno) 40 (3) (2004), 219-227. Zbl1117.34005
3. [3] J.P. Aubin and A. Cellina, Differential inclusions. Set-valued maps and viability theory, Fundamental Principles of Mathematical Sciences, 264, Springer-Verlag, Berlin 1984. 
4. [4] E.P. Avgerinos, N.S. Papageorgiou and N. Yannakakis, Periodic solutions for second order differential inclusions with nonconvex and unbounded multifunction, Acta Math. Hungar. 83 (4) (1999), 303-314. Zbl0939.34013
5. [5] R. Bader, B.D. Gelḿan, M. Kamenskii and V. Obukhovskii, On the topological dimension of the solutions sets for some classes of operator and differential inclusions, Discuss. Math. Differ. Incl. Control Optim. 22 (1) (2002), 17-32. Zbl1041.47031
6. [6] M. Benchora and S.K. Ntouyas, Multi point boundary value problems for second order differential inclusions, Mat. Vesnik 53 (1-2) (2001), 51-58. Zbl1213.34021
7. [7] M. Benchohra and S.K. Ntouyas, On three and four point boundary value problems for second order differential inclusions, Math. Notes (Miskolc) 2 (2) (2001), 93-101. Zbl1010.34005
8. [8] M. Benchohra and S.K. Ntouyas, Multi-point boundary value problems for lower semicontinuous differential inclusions, Math. Notes (Miskolc) 3 (2) (2002), 91-99. Zbl1017.34012
9. [9] A. Boucherif and B. Chanane, Boundary value problems for second order differential inclusions, Int. J. Differ. Equ. Appl. 7 (2) (2003), 147-151. Zbl1048.34032
10. [10] A. Boucherif and B. Chanane, Second order multivalued boundary value problems, Comm. Appl. Nonlinear Anal. 11 (1) (2004), 85-91. Zbl1055.34017
11. [11] Y. Daido, M. Ikehata and G. Nakamura, Reconstruction of inclusions for the inverse boundary value problem with mixed type boundary condition, Appl. Anal. 83 (2) (2004), 109-124. Zbl1106.35132
12. [12] B.C. Dhage, On boundary value problems of second order differential inclusions, Discuss. Math. Differ. Incl. Control Optim. 24 (2004), 73-96. Zbl1078.34003
13. [13] T. Donchev and M. Quincampoix, A two point boundary value problem for a class of differential inclusions, J. Nonlinear Convex Anal. 5 (1) (2004), 59-69. Zbl1058.34080
14. [14] L.H. Erbe and W. Krawcewicz, Boundary value problems for second order nonlinear differential inclusions. Qualitative theory of differential equations (Szeged, 1988), 163-171, Colloq. Math. Soc. Janos Bolyai, 53, North-Holland, Amsterdam 1990. 
15. [15] L.H. Erbe and W. Krawcewicz, Boundary value problems for differential inclusions. Differential equations (Colorado Springs, CO, 1989), 115-135, Lecture Notes in Pure and Appl. Math., 127, Dekker, New York 1991. 
16. [16] L.H. Erbe and W. Krawcewicz, Nonlinear boundary value problems for differential inclusions y''∈ F(t,y,y'), Ann. Polon. Math. 54 (3) (1991), 195-226. Zbl0731.34078
17. [17] L. Erbe, R. Ma and C.C. Tisdell, On two point boundary value problems for second order differential inclusions, Dynam. Systems Appl. 15 (1) (2006), 79-88. Zbl1112.34008
18. [18] L. Erbe, C.C. Tisdell and P.J.Y. Wong, On Systems of boundary value problems for differential inclusions, Acta Math. Sinica (in press). Zbl1126.34012
19. [19] M. Filippakis, L. Gasiński and N.S. Papageorgiou, Positive solutions for second order multivalued boundary value problems, Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday, Vol. 1, 2, 531-547, Kluwer Acad. Publ., Dordrecht 2003. Zbl1051.34013
20. [20] L. Gasiński and N.S. Papageorgiou, Strongly nonlinear multivalued boundary value problems, Nonlinear Anal. 52 (4) (2003), 1219-1238. Zbl1034.34017
21. [21] L. Gasiński and N.S. Papageorgiou, Nonlinear second-order multivalued boundary value problems, Proc. Indian Acad. Sci. Math. Sci. 113 (3) (2003), 293-319. Zbl1052.34022
22. [22] Y.E. Gliklikh and A.V. Obukhovskiĭ, On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds, Abstr. Appl. Anal. (2003), no. 10, 591-600. Zbl1034.58005
23. [23] A.M. Gomaa, On the solution sets of three-point boundary value problems for nonconvex differential inclusions, J. Egyptian Math. Soc. 12 (2) (2004), 97-107. Zbl1089.34011
24. [24] A. Granas and J. Dugundji, Fixed point theory, Springer Monographs in Mathematics, Springer-Verlag, New York 2003. Zbl1025.47002
25. [25] N. Halidias and N.S. Papageorgiou, Existence and relaxation results for nonlinear second-order multivalued boundary value problems in $R^N$, J. Differential Equations 147 (1) (1998), 123-154. Zbl0912.34020
26. [26] D.A. Kandilakis and N.S. Papageorgiou, Existence theorems for nonlinear boundary value problems for second order differential inclusions, J. Differential Equations 132 (1) (1996), 107-125. Zbl0859.34011
27. [27] M. Kisielewicz, Differential inclusions and optimal control, Mathematics and its Applications (East European Series), 44. Kluwer Academic Publishers Group, Dordrecht; PWN - Polish Scientific Publishers, Warsaw 1991. 
28. [28] T. Pruszko, Some applications of the topological degree theory to multivalued boundary value problems, Dissertationes Math. (Rozprawy Mat.) 229 (1984). Zbl0543.34008
29. [29] S. Sędziwy, Fredholm alternative and boundary value problems, Proc. Amer. Math. Soc. 132 (6) (2004), 1779-1784. Zbl1054.34035
30. [30] G.V. Smirnov, Introduction to the theory of differential inclusions, Graduate Studies in Mathematics, 41, American Mathematical Society, Providence, RI 2002. Zbl0992.34001
31. [31] A.N. Vityuk, Solvability of a three-point boundary value problem for a second-order differential inclusion, (Russian) UkraŻn. Mat. Zh. 55 (1) (2003), 132-137; translation in Ukrainian Math. J. 55 (1) (2003), 164-170.