Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
hyperbolic inclusion; measure of noncompactness; measurable multifunction; upper and lower semicontinuous multifunctions; fixed point
hyperbolic inclusion; measure of noncompactness; measurable multifunction; upper and lower semicontinuous multifunctions; fixed point
Summary:
In this paper we examine nonlinear hyperbolic inclusions in Banach spaces. With the aid of a compactness condition involving the ball measure of noncompactness we prove two existence theorems. The first for problems with convex valued orientor fields and the second for problems with nonconvex valued ones.
References:
[1] Banas, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Marcel-Dekker, New York, 1980. MR 0591679
[2] Beckenback, E., Bellman, R.: Inequalities. Springer, Berlin, 1961. MR 0158038
[3] Bressan, A., Colombo, G.: Extensions and selections of maps with decomposable values. Studia Math. 90 (1988), 69-86. MR 0947921
[4] De Blasi, F., Myjak, J.: On the Structure of the set of solutions of the Darboux problem for hyperbolic equations. Proc. Edinburgh Math. Soc. 29 (1986), 7-14. MR 0829175
[5] Hewitt, E., Stromberg, K.: Real and Abstract Analysis. Springer, New York, 1965. MR 0367121
[6] Kandilakis, D., Papageorgiou, N.S.: On the properties of the Aumann integral with applications to differential inclusions and optimal control. Czechoslovak Math. Jour. 39 (1989), 1-15. MR 0983479
[7] Kandilakis, D., Papageorgiou, N.S.: Properties of measurable multifunctions with stochastic domain and their applications. Math. Japonica 35 (1990), 629-643. MR 1067862
[8] Klein, E., Thompson, A.: Theory of Correspondences. Wiley, New York, 1984. MR 0752692
[9] Kubiaczyk, I.: Kneser’s theorem for hyperbolic equations. Functiones et Approximatio 14 (1984), 183-196. MR 0817358
[10] Mönch, H.: Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. Nonlin. Anal-TMA 4 (1980), 985-999. MR 0586861
[11] Papageorgiou, N.S.: On the theory of Banach space valued integrable multifunctions Part 1: Integration and conditional expectation. J. Multiv. Anal. 17 (1985), 185-206. MR 0808276
[12] Papageorgiou, N.S.: Convergence theorems for Banach space valued integrable multifunctions. Intern. J. Math. Sci. 10 (1987), 433-442. MR 0896595 | Zbl 0619.28009
[13] Tarafdar, E., Vyborny, R.: Fixed point theorems for condensing multivalued mappings on a locally convex topological space. Bull. Austr. Math. Soc. 12 (1975), 161-170. MR 0383167
[14] Wagner, D.: Survey of measurable selection theorems. SIAM J. Control and Optim. 15 (1977), 859-903. MR 0486391 | Zbl 0407.28006
[15] Wilansky, A.: Modern Methods in Topological Vector Spaces. McGraw-Hill, New York, 1978. MR 0518316 | Zbl 0395.46001
Search
Partner of
