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Title: A bound sets technique for Dirichlet problem with an upper-Carathéodory right-hand side (English)
Author: Pavlačková, Martina
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 49
Issue: 2
Year: 2010
Pages: 95-106
Summary lang: English
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Category: math
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Summary: In this paper, the existence and the localization result will be proven for vector Dirichlet problem with an upper-Carathéodory right-hand side. The result will be obtained by combining the continuation principle with bound sets technique. (English)
Keyword: Dirichlet problem
Keyword: upper-Carathéodory differential inclusions
Keyword: bounding functions
MSC: 34A60
MSC: 34B15
idZBL: Zbl 1237.34024
idMR: MR2796950
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Date available: 2011-02-18T07:40:04Z
Last updated: 2013-09-18
Stable URL: http://hdl.handle.net/10338.dmlcz/141420
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Reference: [1] Andres, J., Górniewicz, L.: Topological Fixed Point Principles for Boundary Value Problems. Topological Fixed Point Theory and Its Applications, vol. 1 Kluwer, Dordrecht, 2003. Zbl 1029.55002, MR 1998968
Reference: [2] Andres, J., Pavlačková, M.: Asymptotic boundary value problems for second-order differential systems. Nonlin. Anal. 71, 5–6 (2009), 1462–1473. Zbl 1182.34038, MR 2524361, 10.1016/j.na.2008.12.013
Reference: [3] Appell, J., De Pascale, E., Thái, N. H., Zabreiko, P. P.: Multi-Valued Superpositions. Diss. Math., Vol. 345, PWN, Warsaw, 1995. MR 1354934
Reference: [4] De Blasi, F. S., Pianigiani, G.: Solution sets of boundary value problems for nonconvex differential inclusions. Topol. Methods Nonlinear Anal. 1 (1993), 303–314. Zbl 0785.34018, MR 1233098
Reference: [5] Deimling, K.: Multivalued Differential Equations. de Gruyter, Berlin, 1992. Zbl 0820.34009, MR 1189795
Reference: [6] Erbe, L., Krawcewicz, W.: Nonlinear boundary value problems for differential inclusions $y^{\prime \prime } \in F(t, y, y^{\prime })$. Ann. Pol. Math. 54 (1991), 195–226. Zbl 0731.34078, MR 1114171
Reference: [7] Gaines, R., Mawhin, J.: Coincidence Degree and Nonlinear Differential Equations. Springer, Berlin, 1977. Zbl 0339.47031, MR 0637067
Reference: [8] Halidias, N., Papageorgiou, N. S.: Existence and relaxation results for nonlinear second order multivalued boundary value problems in $R^n$. J. Diff. Equations 147 (1998), 123–154. MR 1632661, 10.1006/jdeq.1998.3439
Reference: [9] Halidias, N., Papageorgiou, N. S.: Existence of solutions for quasilinear second order differential inclusions with nonlinear boundary conditions. J. Comput. Appl. Math. 113 (2000), 51–64. Zbl 0941.34008, MR 1735812, 10.1016/S0377-0427(99)00243-5
Reference: [10] Kožušníková, M.: A bounding functions approach to multivalued Dirichlet problem. Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 55 (2007), 1–19. Zbl 1202.34036, MR 2458792
Reference: [11] Kyritsi, S., Matzakos, N., Papageorgiou, N. S.: Nonlinear boundary value problems for second order differential inclusions. Czechoslovak Math. J. 55 (2005), 545–579. Zbl 1081.34020, MR 2153083, 10.1007/s10587-005-0046-5
Reference: [12] Miklaszewski, D.: The two-point problem for nonlinear ordinary differential equations and differential inclusions. Univ. Iagell Acta Math. 36 (1998), 127–132. Zbl 1002.34011, MR 1661330
Reference: [13] Palmucci, M., Papalini, F.: Periodic and boundary value problems for second order differential inclusions. J. of Applied Math. and Stoch. Anal. 14 (2001), 161–182. Zbl 1014.34009, MR 1838344, 10.1155/S1048953301000120
Reference: [14] Zuev, A. V.: On the Dirichlet problem for a second-order ordinary differential equation with discontinuous right-hand side. Diff. Urav. 42 (2006), 320–326. Zbl 1133.34309, MR 2290542
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