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2016 | 36 | 2 | 131-140
Tytuł artykułu

Existence of solutions for a second order problem on the half-line via Ekeland's variational principle

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Abstrakty
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In this paper we study the existence of nontrivial solutions for a nonlinear boundary value problem posed on the half-line. Our approach is based on Ekeland’s variational principle.
Twórcy
autor
  • Laboratory of Fixed Point Theory and Applications Department of Mathematics E.N.S. Kouba, Algiers, Algeria
autor
  • Laboratory of Fixed Point Theory and Applications Department of Mathematics E.N.S. Kouba, Algiers, Algeria
autor
  • School of Mathematics, Statistics and Applied Mathematics National University of Ireland Galway, Ireland
Bibliografia
  • [1] M. Badiale and E. Serra, Semilinear Elliptic Equations for Beginners (Universitext, Springer, London, 2011) x+199 pp.
  • [2] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations (Springer, 2010). doi: 10.1007/978-0-387-70914-7
  • [3] H. Chen, Z. He and J. Li, Multiplicity of solutions for impulsive differential equation on the half-line via variational methods, Bound. Value Probl. 14 (2016). doi: 10.1186/s13661-016-0524-8
  • [4] B. Dai and D. Zhang, The Existence and multiplicity of solutions for second-order impulsive differential equations on the half-line, Results. Math. 63 (2013), 135-149. doi: 10.1007/s00025-011-0178-x
  • [5] S. Djebali and T. Moussaoui, A class of second order BVPs on infinite intervals, Electron. J. Qual. Theory Differ. Equ. (4) (2006), 1-19. doi: 10.14232/ejqtde.2006.1.4
  • [6] S. Djebali, O. Saifi and S. Zahar, Singular boundary value problems with variable coefficients on the positive half-line, Electron. J. Differential Equations 2013 (73) (2013), 1-18.
  • [7] S. Djebali, O. Saifi and S. Zahar, Upper and lower solutions for BVPs on the half-line with variable coefficient and derivative depending nonlinearity, Electron. J. Qual. Theory Differ. Equ. (14) (2011), 1-18. doi: 10.14232/ejqtde.2011.1.14
  • [8] S. Djebali and S. Zahar, Bounded solutios for a derivative dependent boundary value problem on the half-line, Dynam. Systems Appl. 19 (2010), 545-556.
  • [9] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324-353. doi: 10.1016/0022-247X(74)90025-0
  • [10] O. Frites, T. Moussaoui and D. O'Regan, Existence of solutions via variational methods for a problem with nonlinear boundary conditions on the half-line, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 22 (2015), 395-407.
  • [11] H. Lian and W. Ge, Solvability for second-order three-point boundary value problems on a half-line, Appl. Math. Lett. 19 (2006), 1000-1006. doi: 10.1016/j.aml.2005.10.018
  • [12] D. O'Regan, B. Yan and R.P. Agarwal, Nonlinear boundary value problems on semi-infinite intervals using weighted spaces: An upper and lower solution approach, Positivity 11 (2007), 171-189. doi: 10.1007/s11117-006-0050-5
  • [13] N.S. Papageorgiou and S.K. Yiallourou, Handbook of Applied Analysis (Springer, New-York, 2009).
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1187
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