Voir la notice de l'article provenant de la source Library of Science
@article{DMDICO_2002_22_1_a0, author = {Benchohra, Mouffak and Ntouyas, Sotiris}, title = {An existence theorem for an hyperbolic differential inclusion in {Banach} spaces}, journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization}, pages = {5--16}, publisher = {mathdoc}, volume = {22}, number = {1}, year = {2002}, zbl = {1039.35148}, language = {en}, url = {http://geodesic.mathdoc.fr/item/DMDICO_2002_22_1_a0/} }
TY - JOUR AU - Benchohra, Mouffak AU - Ntouyas, Sotiris TI - An existence theorem for an hyperbolic differential inclusion in Banach spaces JO - Discussiones Mathematicae. Differential Inclusions, Control and Optimization PY - 2002 SP - 5 EP - 16 VL - 22 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DMDICO_2002_22_1_a0/ LA - en ID - DMDICO_2002_22_1_a0 ER -
%0 Journal Article %A Benchohra, Mouffak %A Ntouyas, Sotiris %T An existence theorem for an hyperbolic differential inclusion in Banach spaces %J Discussiones Mathematicae. Differential Inclusions, Control and Optimization %D 2002 %P 5-16 %V 22 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/DMDICO_2002_22_1_a0/ %G en %F DMDICO_2002_22_1_a0
Benchohra, Mouffak; Ntouyas, Sotiris. An existence theorem for an hyperbolic differential inclusion in Banach spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 22 (2002) no. 1, pp. 5-16. http://geodesic.mathdoc.fr/item/DMDICO_2002_22_1_a0/
[1] L. Byszewski, Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation $u''_{xt} = F(x,t,u,u_x)$, J. Appl. Math. Stoch. Anal. 3 (3) (1990), 163-168.
[2] L. Byszewski, Theorem about existence and uniqueness of continuous solution of nonlocal problem for nonlinear hyperbolic equation, Appl. Anal. 40 (1991), 173-180.
[3] L. Byszewski and V. Lakshmikantham, Monotone iterative technique for nonlocal hyperbolic differential problem, J. Math. Phys. Sci. 26 (4) (1992), 345-359.
[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.
[5] C. Corduneanu, Integral Equations and Applications, Cambridge Univ. Press, New York 1990.
[6] M. Dawidowski and I. Kubiaczyk, An existence theorem for the generalized hyperbolic equation $z''_{xy} ∈ F(x,y,z)$ in Banach space, Ann. Soc. Math. Pol. Ser. I, Comment. Math. 30 (1) (1990), 41-49.
[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] M. Dawidowski and I. Kubiaczyk, On bounded solutions of hyperbolic differential inclusion in Banach spaces, Demonstr. Math. 25 (1-2) (1992), 153-159.
[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.
[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.
[11] K. Deimling, Multivalued Differential Equations, Walter de Gruyter, Berlin-New York 1992.
[12] J. Dugundji and A. Granas, Fixed Point Theory, Monografie Mat. PWN, Warsaw 1982.
[13] L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, Mathematics and its Applications, 495, Kluwer Academic Publishers, Dordrecht 1999.
[14] S. Heikkila and V. Lakshmikantham, Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, New York 1994.
[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.
[16] I. Kubiaczyk, Kneser's theorem for hyperbolic equations, Funct. Approx. Comment. Math. 14 (1984), 183-196.
[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.
[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.
[19] T.W. Ma, Topological degrees for set-valued compact vector fields in locally convex spaces, Dissertationess Math. 92 (1972), 1-43.
[20] N.S. Papageorgiou, Existence of solutions for hyperbolic differential inclusions in Banach spaces, Arch. Math. (Brno) 28 (1992), 205-213.
[21] H. Schaefer, Über die methode der a priori schranken, Math. Ann. 129 (1955), 415-416.
[22] K. Yosida, Functional Analysis, 6th edn. Springer-Verlag, Berlin 1980.