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Abstract and Applied Analysis
Volume 2006 (2006), Article ID 51794, 21 pages
doi:10.1155/AAA/2006/51794
An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations
1Faculty of Mathematics, Voronezh University, Voronezh 394006, Russia
2Diparimento di Energetica S. Stecco, Universita' di Firenze, Firenze 50139, Italy
Received 26 June 2005; Accepted 1 July 2005
Copyright © 2006 Valeri Obukhovskii et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- Yu. G. Borisovich, B. D. Gelman, A. D. Myšhkis, and V. Obukhovskii, “Topological methods in the theory of fixed points of multivalued mappings,” Uspekhi Matematicheskikh Nauk, vol. 35, no. 1(211), pp. 59–129, 1980, English translation: Russian Mathematical Surveys \textbf{35} (1980), 65–143. View at Zentralblatt MATH · View at MathSciNet
- Yu. G. Borisovich, B. D. Gelman, A. D. Myšhkis, and V. Obukhovskii, Introduction to the Theory of Multivalued Maps and Differential Inclusions, KomKniga, Moscow, 2005.
- Yu. G. Borisovich, V. Zvyagin, and Y. I. Sapronov, “Nonlinear Fredholm mappings, and Leray-Schauder theory,” Uspekhi Matematicheskikh Nauk, vol. 32, no. 4(196), pp. 3–54, 1977, English translation in Russian Mathematical Surveys \textbf{32} (1977), no. 4, 1–54. View at MathSciNet
- Yu. G. Borisovich, V. Zvyagin, and V. V. Shabunin, “On the solvability in of the nonlinear Dirichlet problem in a narrow strip,” Doklady Akademii Nauk, vol. 334, no. 6, pp. 683–685, 1994, English translation in Russian Academy of Sciences Doklady Mathematics \textbf{49} (1994), no. 1, 179–182. View at Zentralblatt MATH · View at MathSciNet
- K. Borsuk, Theory of Retracts, vol. 44 of Monografie Matematyczne, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. View at Zentralblatt MATH · View at MathSciNet
- K. Deimling, Multivalued Differential Equations, vol. 1 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, 1992. View at Zentralblatt MATH · View at MathSciNet
- D. Gabor, “The coincidence index for fundamentally contractible multivalued maps with nonconvex values,” Annales Polonici Mathematici, vol. 75, no. 2, pp. 143–166, 2000. View at Zentralblatt MATH · View at MathSciNet
- D. Gabor and W. Kryszewski, “A coincidence theory involving Fredholm operators of nonnegative index,” Topological Methods in Nonlinear Analysis, vol. 15, no. 1, pp. 43–59, 2000. View at Zentralblatt MATH · View at MathSciNet
- L. Górniewicz, Topological Fixed Point Theory of Multivalued Mappings, vol. 495 of Mathematics and Its Applications, Kluwer Academic, Dordrecht, 1999. View at Zentralblatt MATH · View at MathSciNet
- L. Górniewicz, A. Granas, and W. Kryszewski, “On the homotopy method in the fixed point index theory of multi-valued mappings of compact absolute neighborhood retracts,” Journal of Mathematical Analysis and Applications, vol. 161, no. 2, pp. 457–473, 1991. View at Zentralblatt MATH · View at MathSciNet
- D. M. Hyman, “On decreasing sequences of compact absolute retracts,” Fundamenta Mathematicae, vol. 64, pp. 91–97, 1969. View at Zentralblatt MATH · View at MathSciNet
- M. Kamenskii, V. Obukhovskii, and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, vol. 7 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, 2001. View at Zentralblatt MATH · View at MathSciNet
- S. V. Kornev and V. Obukhovskii, “On some versions of the topological degree theory for nonconvex-valued multimaps,” Trudy Matematicheskogo Fakul'teta. Novaya Seriya, vol. 8, pp. 56–74, 2004 (Russian).
- M. A. Krasnosel'skiĭ and P. P. Zabreĭko, Geometrical Methods of Nonlinear Analysis, vol. 263 of Fundamental Principles of Mathematical Sciences, Springer, Berlin, 1984. View at Zentralblatt MATH · View at MathSciNet
- A. D. Myshkis, “Generalizations of the theorem on a fixed point of a dynamical system inside of a closed trajectory,” Matematicheskiĭ Sbornik. Novaya Seriya, vol. 34(76), pp. 525–540, 1954 (Russian). View at MathSciNet
- V. Obukhovskii, “Some fixed point principles for multivalued condensing operators,” Trudy Matematicheskogo Fakul'teta. Voronezhskij Gosudarstvennyj Universitet, no. 4, pp. 70–79, 1970 (Russian). View at MathSciNet
- V. Obukhovskii, P. Zecca, and V. Zvyagin, “On coincidence index for multivalued perturbations on nonlinear Fredholm maps and some applications,” Abstract and Applied Analysis, vol. 7, no. 6, pp. 295–322, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- T. Pruszko, “A coincidence degree for -compact convex-valued mappings and its application to the Picard problem of orientor,” L'Acadéemie Polonaise des Sciences. Bulletin. Séerie des Sciences Mathéematiques, vol. 27, no. 11-12, pp. 895–902 (1981), 1979. View at Zentralblatt MATH · View at MathSciNet
- E. Tarafdar and S. K. Teo, “On the existence of solutions of the equation and a coincidence degree theory,” Journal of Australian Mathematical Society. Series A, vol. 28, no. 2, pp. 139–173, 1979. View at Zentralblatt MATH · View at MathSciNet
- V. G. Zvjagin, “The existence of a continuous branch for the eigenfunctions of a nonlinear elliptic boundary value problem,” Differencial'nye Uravnenija, vol. 13, no. 8, pp. 1524–1527, 1977 (Russian). View at MathSciNet
- V. Zvyagin, “The oriented degree of a class of perturbations of Fredholm mappings and the bifurcation of the solutions of a nonlinear boundary value problem with noncompact perturbations,” Matematicheskij Sbornik, vol. 182, no. 12, pp. 1740–1768, 1991 (Russian), English translation in Mathematics of the USSR, Sbornik \textbf{74} (1993), no. 2, 487–512. View at Zentralblatt MATH · View at MathSciNet
- V. Zvyagin and N. M. Ratiner, “Oriented degree of Fredholm maps of nonnegative index and its application to global bifurcation of solutions,” in Global Analysis—Studies and Applications, V, vol. 1520 of Lecture Notes in Math., pp. 111–137, Springer, Berlin, 1992. View at MathSciNet