An existence theorem for an hyperbolic differential inclusion in Banach spaces

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1. [1] L. Byszewski, Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation $u_{xt}^{\text{'}\text{'}}=F(x,t,u,u_x)$, J. Appl. Math. Stoch. Anal. 3 (3) (1990), 163-168. Zbl0725.35059
2. [2] L. Byszewski, Theorem about existence and uniqueness of continuous solution of nonlocal problem for nonlinear hyperbolic equation, Appl. Anal. 40 (1991), 173-180. Zbl0725.35060
3. [3] L. Byszewski and V. Lakshmikantham, Monotone iterative technique for nonlocal hyperbolic differential problem, J. Math. Phys. Sci. 26 (4) (1992), 345-359. Zbl0811.35083
4. [4] L. Byszewski and N.S. Papageorgiou, An application of a noncompactness technique to an investigation of the existence of solutions to nonlocal multivalued Darboux problem, J. Appl. Math. Stoch. Anal. 12 (2) (1999), 179-190. Zbl0936.35203
5. [5] C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press, New York 1990. 
6. [6] M. Dawidowski and I. Kubiaczyk, An existence theorem for the generalized hyperbolic equation $z_{xy}^{\text{'}\text{'}}\in F(x,y,z)$ in Banach space, Ann. Soc. Math. Pol. Ser. I, Comment. Math. 30 (1) (1990), 41-49. Zbl0759.35029
7. [7] M. Dawidowski and I. Kubiaczyk, Existence theorem for hyperbolic differential inclusion with Carathéodory right hand side, Discuss. Math. Differ. Incl. 10 (1990), 69-75. 
8. [8] M. Dawidowski and I. Kubiaczyk, On bounded solutions of hyperbolic differential inclusion in Banach spaces, Demonstr. Math. 25 (1-2) (1992), 153-159. 
9. [9] F. De Blasi and J. Myjak, On the structure of the set of solutions of the Darboux problem for hyperbolic equations, Proc. Edinburgh Math. Soc. 29 (1986), 7-14. Zbl0594.35069
10. [10] F. De Blasi and J. Myjak, On the set of solutions of a differential inclusion, Bull. Inst. Math., Acad. Sin. 14 (1986), 271-275. Zbl0607.34010
11. [11] K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin-New York 1992. Zbl0760.34002
12. [12] J. Dugundji and A. Granas, Fixed Point Theory, Monografie Mat. PWN, Warsaw 1982. 
13. [13] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht 1999. Zbl0937.55001
14. [14] S. Heikkila and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York 1994. Zbl0804.34001
15. [15] Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory, Kluwer, Dordrecht, Boston, London, 1997, Volume II: Applications, Kluwer, Dordrecht, Boston, London 2000. Zbl0887.47001
16. [16] I. Kubiaczyk, Kneser's theorem for hyperbolic equations, Funct. Approx. Comment. Math. 14 (1984), 183-196. Zbl0555.35092
17. [17] I. Kubiaczyk and A.N. Mostafa, On the existence of weak solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces, Fasc. Math. 28 (1998), 93-99. Zbl0913.35077
18. [18] 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
19. [19] T.W. Ma, Topological degrees for set-valued compact vector fields in locally convex spaces, Dissertationess Math. 92 (1972), 1-43. 
20. [20] N.S. Papageorgiou, Existence of solutions for hyperbolic differential inclusions in Banach spaces, Arch. Math. (Brno) 28 (1992), 205-213. Zbl0781.34045
21. [21] H. Schaefer, Über die methode der a priori schranken, Math. Ann. 129 (1955), 415-416. Zbl0064.35703
22. [22] K. Yosida, Functional Analysis, 6th edn. Springer-Verlag, Berlin 1980.