Existence results for a class of high order differential equation associated with integral boundary conditions at resonance
Le Cong Nhan; Do Huy Hoang; Le Xuan Truong
Archivum Mathematicum (2017)
- Volume: 053, Issue: 2, page 111-130
- ISSN: 0044-8753
Access Full Article
topAbstract
topHow to cite
topNhan, Le Cong, Hoang, Do Huy, and Truong, Le Xuan. "Existence results for a class of high order differential equation associated with integral boundary conditions at resonance." Archivum Mathematicum 053.2 (2017): 111-130. <http://eudml.org/doc/288196>.
@article{Nhan2017,
abstract = {By using Mawhin’s continuation theorem, we provide some sufficient conditions for the existence of solution for a class of high order differential equations of the form \[x^\{(n)\} =f(t,x,x^\{\prime \},\dots ,x^\{(n-1)\})\,, \quad t \in [0, 1]\,,\]
associated with the integral boundary conditions at resonance. The interesting point is that we shall deal with the case of nontrivial kernel of arbitrary dimension corresponding to high order differential operator which will cause some difficulties in constructing the generalized inverse operator.},
author = {Nhan, Le Cong, Hoang, Do Huy, Truong, Le Xuan},
journal = {Archivum Mathematicum},
keywords = {coincidence degree; high order differential equation; resonance},
language = {eng},
number = {2},
pages = {111-130},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence results for a class of high order differential equation associated with integral boundary conditions at resonance},
url = {http://eudml.org/doc/288196},
volume = {053},
year = {2017},
}
TY - JOUR
AU - Nhan, Le Cong
AU - Hoang, Do Huy
AU - Truong, Le Xuan
TI - Existence results for a class of high order differential equation associated with integral boundary conditions at resonance
JO - Archivum Mathematicum
PY - 2017
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 053
IS - 2
SP - 111
EP - 130
AB - By using Mawhin’s continuation theorem, we provide some sufficient conditions for the existence of solution for a class of high order differential equations of the form \[x^{(n)} =f(t,x,x^{\prime },\dots ,x^{(n-1)})\,, \quad t \in [0, 1]\,,\]
associated with the integral boundary conditions at resonance. The interesting point is that we shall deal with the case of nontrivial kernel of arbitrary dimension corresponding to high order differential operator which will cause some difficulties in constructing the generalized inverse operator.
LA - eng
KW - coincidence degree; high order differential equation; resonance
UR - http://eudml.org/doc/288196
ER -
References
top- Du, Z., Lin, X., Ge, W., 10.1016/j.cam.2004.08.003, J. Comput. Appl. Math. 177 (2005), 55–65. (2005) Zbl1059.34010MR2118659DOI10.1016/j.cam.2004.08.003
- Feng, W., Webb, J.R.L., 10.1006/jmaa.1997.5520, J. Math. Anal. Appl. 212 (1997), 467–480. (1997) Zbl0883.34020MR1464891DOI10.1006/jmaa.1997.5520
- Feng, W., Webb, J.R.L., 10.1016/S0362-546X(96)00118-6, Nonlinear Anal. 30 (6) (1997), 3227–3238. (1997) Zbl0891.34019MR1603039DOI10.1016/S0362-546X(96)00118-6
- Franco, D., Infante, G., Zima, M., 10.1002/mana.200810841, Math. Nachr. 284 (2011), 875–884. (2011) Zbl1273.34029MR2815958DOI10.1002/mana.200810841
- Gaines, R.E., Mawhin, J., 10.1007/BFb0089537, Lecture Notes in Math., vol. 568, Springer Verlag Berlin, 1977. (1977) Zbl0339.47031MR0637067DOI10.1007/BFb0089537
- Gao, Y., Pei, M., Solvability for two classes of higher-order multi-point boundary value problems at resonance, Boundary Value Problems (2008), Art. ID 723828, 14 pp. (2008) Zbl1149.34008MR2392915
- Gupta, C.P., 10.1155/S0161171295000901, Internat. J. Math. Math. Sci. 18 (4) (1995), 705–710. (1995) Zbl0839.34027MR1347059DOI10.1155/S0161171295000901
- Il’in, V.A., Moiseev, E.I., Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator, J. Differential Equations 23 (1987), 803–810. (1987) MR0903975
- Il’in, V.A., Moiseev, E.I., Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator, J. Differential Equations 23 (1987), 979–978. (1987) Zbl0668.34024MR0909590
- Infante, G., Zima, M., 10.1016/j.na.2007.08.024, Nonlinear Anal. 69 (2008), 622–633. (2008) Zbl1203.34041MR2446343DOI10.1016/j.na.2007.08.024
- Kosmatov, N., 10.1016/j.na.2005.09.042, Nonlinear Anal. 65 (2006), 622–633. (2006) Zbl1121.34023MR2231078DOI10.1016/j.na.2005.09.042
- Kosmatov, N., 10.1016/j.jmaa.2012.04.069, J. Math. Anal. Appl. 394 (2012), 425–431. (2012) Zbl1260.34037MR2926233DOI10.1016/j.jmaa.2012.04.069
- Lin, X., Du, Z., Ge, W., 10.1016/j.camwa.2005.01.001, Comput. Math. Appl. 49 (2005), 1–11. (2005) Zbl1081.34017MR2123180DOI10.1016/j.camwa.2005.01.001
- Lu, S., Ge, W., 10.1016/S0022-247X(03)00567-5, J. Math. Anal. Appl. 287 (2003), 522–539. (2003) Zbl1046.34029MR2024338DOI10.1016/S0022-247X(03)00567-5
- Ma, R., 10.1016/j.jmaa.2004.02.005, J. Math. Anal. Appl. 294 (2004), 147–157. (2004) Zbl1070.34028MR2059796DOI10.1016/j.jmaa.2004.02.005
- Mawhin, J., Topological degree methods in nonlinear boundary value problems, Expository lectures from the CBMS Regional Conference held at Harvey Mudd College, Claremont, Calif., June 9–15, 1977. CBMS Regional Conference Series in Mathematics, 40, American Mathematical Society, Providence, R.I., 1979. (1979) Zbl0414.34025MR0525202
- Mawhin, J., Functional analysis and nonlinear boundary value problems: the legacy of Andrzej Lasota, Ann. Math. Sil. 27 (2013), 7–38. (2013) Zbl1326.34013MR3157115
- O’Regan, D., 10.1090/S0002-9939-1991-1069295-2, Proc. Amer. Math. Soc. 113 (1991), 761–775. (1991) Zbl0742.34023MR1069295DOI10.1090/S0002-9939-1991-1069295-2
- Przeradzki, B., Three methods for the study of semilinear equations at resonance, Colloq. Math. (1993), 110–129. (1993) Zbl0828.47054MR1242650
- Wong, F.H., 10.1090/S0002-9939-98-04709-1, Proc. Amer. Math. Soc. 126 (1998), 2389–2397. (1998) MR1476399DOI10.1090/S0002-9939-98-04709-1
- Zhang, X., Feng, M., Ge, W., 10.1016/j.jmaa.2008.11.082, J. Math. Anal. Appl. 353 (2009), 311–319. (2009) Zbl1180.34016MR2508869DOI10.1016/j.jmaa.2008.11.082
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.