An application of the fixed point theorem of Bohnenblust-Karlin to the Darboux problem for a multivalued inclusion

Georgeta Teodoru

doi:10.33993/jnaat292-672

Authors

Georgeta Teodoru Technical University Iasi, Romania

DOI:

https://doi.org/10.33993/jnaat292-672

Abstract views: 222

Abstract

Not available.

Downloads

Download data is not yet available.

References

Aumann, R. J., Integrals of set-valued functions, J. Math. Anal. Appl., 12, pp. 1-12, 1965, https://doi.org/10.1016/0022-247x(65)90049-1 DOI: https://doi.org/10.1016/0022-247X(65)90049-1

Bohnenblust, H. F. and Karlin, S., On a theorern of Ville, Contrib. to theory of games, I. Ann. Math. Studies, 24, Princeton University Press, Princeton N.J., pp. 155-160, 1950, https://doi.org/10.1515/9781400881727-014 DOI: https://doi.org/10.1515/9781400881727-014

De Blas, F.S. and Myjak, J., On the set of solutions of a differential inclusion, Bulletin of the Institute of Mathematics, Academia Sinica, 14, no. 3, pp. 271-275, 1986.

Hermes, H., The generalized differential equation x ∈RR(t,x), Advances in mathematics, 4, pp. 149-169, 1970, https://doi.org/10.1016/0001-8708(70)90020-4 DOI: https://doi.org/10.1016/0001-8708(70)90020-4

Hermes, H., On continuous and measurable selections and the existence of solutions of generalized differential equations, Proceedings of the American Mathematical Society, 29, no. 3, pp. 535-542,1971, https://doi.org/10.2307/2038593 DOI: https://doi.org/10.1090/S0002-9939-1971-0277794-3

Himmelberg, C.J. and Van Vleck, F.S., Lipschitzian generalized differential equations, Rend. Sem. Mat. Univ. Padova, 48, pp. 159-169, 1973.

Istrătescu, V. I., Introducere în teoria punctelor fixre, Editura Academiei Române, Bucureşti, 1973 (in Romanian).

Kubiaczyk, I., Existence theorem for multivalued hyperbolic equation, Annales Societatis Mathematicae Polonae, Series I: Commentationes Mathematicae, 27, pp. 115-119, 1987.

Marano, S. 4., Generalized, solutions of partial differential inclusions depending on a parameter, Rendiconti Accademia Nazionale delle Scienze detta dei XL, Memorie di matematica 107⁰, 13, 18, pp. 281-295, 1989.

Marano, S. 4., Classical solutions of partial differential inclusions in Banach spaces, Applicable Analysis, 42, no. 2, pp.127-143, 1991, https://doi.org/10.1080/00036819108840037 DOI: https://doi.org/10.1080/00036819108840037

Michael, E., Topologies on spaces of subsets, Am. Math. Soc. T!ansl., 71, pp. 152-182, 1951, https://doi.org/10.1090/s0002-9947-1951-0042109-4 DOI: https://doi.org/10.1090/S0002-9947-1951-0042109-4

Pruszko,T., Topological degree methods in multivalued boundary value problems, Nonlinear Analysis, Theory, Methods & Applications, 5, no. 9, pp. 959-973, 1981, https://doi.org/10.1016/0362-546x(81)90056-0 DOI: https://doi.org/10.1016/0362-546X(81)90056-0

Rus, I. A., Principii şi aplicaţii ale teoriei punctului fix, Editura Dacia, Cluj-Napoca, 1979 (in Romanian).

Sosulski, W., Existence theorem for generalized functional-differential equations of hyperbolic type, Annales Societatis Mathematicae Polonae, Series I: Commentationes Mathematicae, 25, pp. 149-152, 1985.

Sosulski, W., On neutral partial functional-differential inclusions of hiperbolic type, Demonstratio Mathematica, 23, no. 4, pp. 893-909, 1990. DOI: https://doi.org/10.1515/dema-1990-0408

Staicu, Y., WeII posedness for differential inclusions, Ph. D. Thesis, Sissa, Trieste, 1989/1990.

Staicu ,Y ., On a non-convex hyperbolic differential inclusion, Proceedings of the Edinburgh Mathematical Society, 35, pp. 376-382, 1992, https://doi.org/10.1017/s0013091500005666 DOI: https://doi.org/10.1017/S0013091500005666

Teodoru, G., Studiul soluţiilor ecuaţiilor de forma ∂z/∂x∂y∈F(x,y,y),Teză de doctorat, Universitatea "Al. I. Cuza" Iaşi, 1984.

Teodoru, G., Le problème de Darboux pour une équation aux derivées partielles multivoque, Analele Şt. Univ. "Al. I. Cuza" Iaşi, 31, S.I.a Mat., no.2, pp. 173-176, 1985.

Teodoru, G., Sur Ie problème de Darboux pour l'équation ∂z/∂x∂y∈F(x,y,y), Analele Şt. Univ. "Al.L Cuza" Iaşi, 32, S.I.a Mat., no. 3, pp. 41-49, 1986.

Teodoru, G., A characterization of the solutions of the Darboux problem for the equation ∂z/∂x∂y∈F(x,y,y), Analele Şt. Univ. "Al.I. Cuza" Iaşi, 33, S.I a Mat., no. 1, pp. 33-38, 1987.

Teodoru, G., Approximation of the solution of the Darboux problem for the equation ∂z/∂x∂y∈F(x,y,y), Arralele Şt. Univ. "Al.I. Cuza" Iaşi, 34, S.I. a Mat., no. 1, pp. 31-36, 1988.

Teodoru, G., Continuous selections for multivalued, functions, Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj- Napoca, pp.273-278, 1986.

Teodoru, G., Continuous selections for multifunctions satisfying the Carathéodory type conditions. The Darboux problem associated, to a multivalued equation, Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, pp. 281-285, 1987.

Teodoru, G., Continuous selections for multifunctions and, the Darboux problem for multivalued, equations, Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, pp. 297-304, 1989.

Teodoru, G., An application of Fryszkowski selection theorem to the Darboux problem for a multivalued, equation Studia Univ. Babeş-Bolyai, Cluj- Napoca, Mathematica, 34, no. 2, pp. 36-40, 1989.

Teodoru, G., An application of the contraction principle of Covitz and Nadler to the Darboux problem for a multivalued equation, Analele Şt. Univ. "AI.L Cuza" Iaşi, 36,no. 2, pp. 99-104, 1990.

Teodoru, G., The Darboux problem associated with Lipschitzian hyperbolic multivalued. equation, Bul. Inst. Polit. Iaşi, 36 (50), f. 1, Secţia I, Matematică, Mecanică teoretică, Fizică, pp. 35-40, 1990.

Teodoru, G., Classi cal solutions of partial functional-differential inclusions in Banach space, 4th International Conference in Applied Mathematics and Mechanics, Cluj-Napoca, June 7-12, 1994, Acta Tech. Napocensis, seria Mat. Apl. şi Mecanică (to appear).

Teodoru, G. and Drăgan, V., The Darboux problem for random hyperbolic multivalued equations, Bul. Univ. Tehnică "Gh. Asachi" , Iaşi, 40 (44), Sectia I, Matematică, Mecanică teoretică, Fizică, 1994 (to appear).

Teodoru, G. and Drăgan,Y., Continuous dependence of parameter of the solutions for differential hyperbolic inclusions, Memoriile Secţiilor Ştiinţifice ale Academiei Române, 1994, (to appear).

Teodoru, G., Classical solutions of partial functional-differential inclusions in Banach space, Studia Univ. Babeş-Bolyai, Cluj-Napoca, 40, 1995 (to appear).

Teodoru, G., Generalized solutions for partial differential functional inclusions depending on a parameter, Bul. Univ. Tehnică "Gh. Asachi", Iaşi, 41 (45), Matematică, Mecanică teoretică, Fizică, 1995 (to appear).

Vitiuc, A. N., On the existence of a class of multivalued partial differential equa- tions. Boundary value problems (Russian), Viniti, 1982, pp. 1-31, "Kraevâie zadaci" (Russian), pp. 131-133, pp. 162-163. Perm. Politekh. Inst' Perm., 1984'