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 |
. |
Category:
|
math |
. |
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 |
. |
Date available:
|
2011-02-18T07:40:04Z |
Last updated:
|
2013-09-18 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141420 |
. |
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 |
. |