Existence of solutions for a class of first order boundary value problems
Amirouche Mouhous a; Svetlin Georgiev Georgiev b; Karima Mebarki c
Archivum Mathematicum (2022)
- Volume: 058, Issue: 3, page 141-158
- ISSN: 0044-8753
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topMouhous a, Amirouche, Georgiev b, Svetlin Georgiev, and Mebarki c, Karima. "Existence of solutions for a class of first order boundary value problems." Archivum Mathematicum 058.3 (2022): 141-158. <http://eudml.org/doc/298344>.
@article{Mouhousa2022,
abstract = {In this work, we are interested in the existence of solutions for a class of first order boundary value problems (BVPs for short). We give new sufficient conditions under which the considered problems have at least one solution, one nonnegative solution and two non trivial nonnegative solutions, respectively. To prove our main results we propose a new approach based upon recent theoretical results. The results complement some recent ones.},
author = {Mouhous a, Amirouche, Georgiev b, Svetlin Georgiev, Mebarki c, Karima},
journal = {Archivum Mathematicum},
keywords = {first order BVPs; nonnegative solution; fixed point index; cone; expansive mapping; sum of operators},
language = {eng},
number = {3},
pages = {141-158},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence of solutions for a class of first order boundary value problems},
url = {http://eudml.org/doc/298344},
volume = {058},
year = {2022},
}
TY - JOUR
AU - Mouhous a, Amirouche
AU - Georgiev b, Svetlin Georgiev
AU - Mebarki c, Karima
TI - Existence of solutions for a class of first order boundary value problems
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 3
SP - 141
EP - 158
AB - In this work, we are interested in the existence of solutions for a class of first order boundary value problems (BVPs for short). We give new sufficient conditions under which the considered problems have at least one solution, one nonnegative solution and two non trivial nonnegative solutions, respectively. To prove our main results we propose a new approach based upon recent theoretical results. The results complement some recent ones.
LA - eng
KW - first order BVPs; nonnegative solution; fixed point index; cone; expansive mapping; sum of operators
UR - http://eudml.org/doc/298344
ER -
References
top- Ascher, U.M., Mattheij, R.M.M., Russell, R.D., Numerical solution of boundary value problems for ordinary differential equations, SIAM Classics Appl. Math. 13 (1995). (1995) MR1351005
- Djebali, S., Mebarki, K., 10.12775/TMNA.2019.055, Topol. Methods Nonlinear Anal. 54 (no 2A) (2019), 613–640, DOI 10.12775/TMNA.2019.055. (2019) MR4061312DOI10.12775/TMNA.2019.055
- Franco, D., Nieto, J.J., O’Regan, D., Anti-periodic boundary value problem for nonlinear first-order differential equations, Math. Inequal. Appl. 6 (2003), 477–485. (2003) MR1992487
- Georgiev, S., Kheloufi, A., Mebarki, K., Classical solutions for the Korteweg-De Vries equation, New trends Nonlinear Anal. Appl., (to appear), 2022. (2022)
- Georgiev, S., Zennir, K., 10.1007/s11587-021-00649-2, Ric. Mat. (2021), https://doi.org/10.1007/s11587-021-00649-2. (2021) MR4440734DOI10.1007/s11587-021-00649-2
- Hong, S., Boundary-value problems for first and second order functional differential inclusions, EJDE 2033 (no 32) (2003), 1–10. (2003) MR1971018
- Peng, S., 10.1016/j.amc.2003.08.090, Appl. Math. Comput. 158 (2004), 345–351. (2004) MR2094624DOI10.1016/j.amc.2003.08.090
- Tisdell, C.C., 10.1016/j.jmaa.2005.11.047, J. Math. Anal. Appl. 323 (2006), 1325–1332. (2006) MR2260183DOI10.1016/j.jmaa.2005.11.047
- Tisdell, C.C., On the solvability of nonlinear first-order boundary value problems, EJDE 2006 (no 80) (2006), 1–8. (2006) MR2240828
- Wang, D.B., Periodic boundary value problems for nonlinear first-order impulsive dynamic equations on time scales, Adv. Difference Equ. 2012 (12) (2012), 9 pp. (2012) MR2915355
- Xiang, T., Yuan, R., 10.1016/j.na.2009.01.197, Nonlinear Anal. 71 (2009), 3229–3239. (2009) MR2532845DOI10.1016/j.na.2009.01.197
- Xing, Y., Fu, Y., Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type, Adv. Difference Equ. 2011 (14) (2011), 17 pp. (2011) MR2824941
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