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A note on the dependence of solutions on functional parameters for nonlinear Sturm-Liouville problems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We deal with the existence and the continuous dependence of solutions on functional parameters for boundary valued problems containing the Sturm-Liouville equation. We apply these result to prove the existence of at least one solution for a certain class of optimal control problems.
Rocznik
Strony
837--849
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • Faculty of Mathematics University of Łódz Banacha 22, 90-238 Łódz, Poland
Bibliografia
  • [1] T. Adamowicz, A. Kałamajska, On a variant of the maximum principle involving radial p-Laplacian with applications to nonlinear eigenvalue problems and nonexistence results, Topol. Methods Nonlinear Anal. 34 (2009) 1, 1–20.
  • [2] T. Adamowicz, A. Kałamajska, Maximum principles and nonexistence results for radial solutions to equations involving p-Laplacian, Math. Methods Appl. Sci. 33 (2010) 13, 1618–1627.
  • [3] R.P. Agarwal, R.S. Grace, D. O’Regan, Oscilation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations, Dordrecht, Kluwer Academic, 2002.
  • [4] R. Dalmasso, Positive solutions of singular boundary value problems, Nonlinear Anal. 27 (1996) 6, 645–652.
  • [5] P. Eloe, J. Henderson, Uniqueness implies existence and uniqueness conditions for a class of (k + j )-point boundary value problems for nth order differential equations, Math. Nachr. 284 (2011) 2–3, 229–239.
  • [6] L. Erbe, T.S. Hassan, A. Peterson, Oscillation of second order neutral delay differential equations, Adv. Dyn. Syst. Appl. 3 (2008) 1, 53–71.
  • [7] A.F. Güvenilir, A. Zafer, Second order oscillation of forced functional differential equations with oscillatory potentials, Comput. Math. Appl. 51 (2006) 9–10, 1395–1404.
  • [8] T.S. Hassan, Interval oscillation for second order nonlinear differential equations with a damping term, Serdica Math. J. 34 (2008) 4, 715–732.
  • [9] T.S. Hassan, L. Erbe, A. Peterson, Forced oscillation of second order differential equations with mixed nonlinearities, Acta Math. Sci. 31 (2011) 2, 613–626.
  • [10] H. Li, Y. Liu, On sign-changing solutions for a second-order integral boundary value problem, Comput. Math. Appl. 62 (2011) 2, 651–656.
  • [11] H. Li, J. Sun, Positive solutions of sublinear Sturm-Liouville problems with changing sign nonlinearity, Comput. Math. Appl. 58 (2009) 9, 1808–1815.
  • [12] E.H. Lieb, M. Loss, Analysis, Graduate Studies in Mathematics, Vol. 14, 1997.
  • [13] Y. Liu, H. Yu, Existence and uniqueness of positive solution for singular boundary value problem, Comput. Math. Appl. 50 (2005) 1–2, 133–143.
  • [14] J. Mawhin, Metody wariacyjne dla nieliniowych problemów Dirichleta, Wydawnictwa Naukowo-Techniczne, Warszawa, 1994 [in Polish].
  • [15] A. Orpel, Nonlinear BVPS with functional parameters, J. Differential Equations 246 (2009) 4, 1500–1522.
  • [16] D. O’Regan, A.Orpel, Eigenvalue intervals for higher order problems with singular nonlinearities, Appl. Math. Comput. 218 (2011) 4, 1233–1239.
  • [17] H. Su, L. Liu, Y. Wu, Positive solutions for Sturm Liouville boundary value problems in a Banach space, Abstr. Appl. Anal. (2012), Art. ID 572172, 11 pp.
  • [18] H. Su, Z. Wei, F. Xu, The existence of positive solutions for nonlinear singular boundary value system with p-Laplacian, Appl. Math. Comput. 181 (2006) 2, 826–836.
  • [19] Z. Wei, Positive solutions of singular Dirichlet boundary value problems at nonresonance, Chinese Ann. Math. Ser. A 20 (1999) 5, 543–552.
  • [20] G. Vidossich, On the continuous dependence of solutions of boundary value problems for ordinary differential equations, J. Differential Equations 82 (1989) 1, 1–14.
  • [21] J. Yang, Z. Wei, K. Liu, Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems, Appl. Math. Comput. 214 (2009) 2, 424–432.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a5a37a3e-6683-4fea-8d3c-1a468b9f274d
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