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Czasopismo

2012 | 10 | 6 | 1969-1980

Tytuł artykułu

On variational impulsive boundary value problems

Autorzy

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
Using the variational approach, we investigate the existence of solutions and their dependence on functional parameters for classical solutions to the second order impulsive boundary value Dirichlet problems with L1 right hand side.

Wydawca

Czasopismo

Rocznik

Tom

10

Numer

6

Strony

1969-1980

Opis fizyczny

Daty

wydano
2012-12-01
online
2012-10-12

Twórcy

  • Institute of Mathematics, Technical University of Łódź, Wólczańska 215, 90-924, Łódź, Poland

Bibliografia

  • [1] Appell J., Zabrejko P.P., Nonlinear Superposition Operators, Cambridge Tracts in Math., 95, Cambridge University Press, Cambridge, 1990 http://dx.doi.org/10.1017/CBO9780511897450[Crossref]
  • [2] Chen H., Li J., Variational approach to impulsive differential equations with Dirichlet boundary conditions, Bound. Value Probl., 2010, #325415 [WoS][Crossref]
  • [3] Feng M., Xie D., Multiple positive solutions of multi-point boundary value problem for second-order impulsive differential equations, J. Comput. Appl. Math., 2009, 223(1), 438–448 http://dx.doi.org/10.1016/j.cam.2008.01.024[Crossref]
  • [4] Idczak D., Rogowski A., On a generalization of Krasnoselskii’s theorem, J. Aust. Math. Soc., 2002, 72(3), 389–394
  • [5] Jankowski T., Positive solutions to second order four-point boundary value problems for impulsive differential equations, Appl. Math. Comput., 2008, 202(2), 550–561 http://dx.doi.org/10.1016/j.amc.2008.02.040[Crossref]
  • [6] Lakshmikantham V., Baĭnov D.D., Simeonov P.S., Theory of Impulsive Differential Equations, Ser. Modern Appl. Math., 6, World Scientific, Teaneck, 1989 http://dx.doi.org/10.1142/0906[Crossref]
  • [7] Ledzewicz U., Schättler H., Walczak S., Optimal control systems governed by second-order ODEs with Dirichlet boundary data and variable parameters, Illinois J. Math., 2003, 47(4), 1189–1206
  • [8] Mawhin J., Problèmes de Dirichlet Variationnels non Linéaires, Sem. Math. Sup., 104, Presses de l’Université de Montréal, Montréal, 1987
  • [9] Nieto J.J., Variational formulation of a damped Dirichlet impulsive problem, Appl. Math. Lett., 2010, 23(8), 940–942 http://dx.doi.org/10.1016/j.aml.2010.04.015[WoS][Crossref]
  • [10] Nieto J.J., O’Regan D., Variational approach to impulsive differential equations, Nonlinear Anal. Real World Appl., 2009, 10(2), 680–690 http://dx.doi.org/10.1016/j.nonrwa.2007.10.022[Crossref]
  • [11] Samoilenko A.M., Perestyuk N.A., Impulsive Differential Equations, World Sci. Ser. Nonlinear Sci. Ser. A Monogr. Treatises, 14, World Scientific, Singapore, 1995
  • [12] Sun J., Chen H., Multiplicity of solutions for a class of impulsive differential equations with Dirichlet boundary conditions via variant fountain theorems, Nonlinear Anal. Real World Appl., 2010, 11(5), 4062–4071 http://dx.doi.org/10.1016/j.nonrwa.2010.03.012[Crossref]
  • [13] Tian Y., Ge W., Applications of variational methods to boundary-value problem for impulsive differential equations, Proc. Edinb. Math. Soc., 2008, 51(2), 509–527 http://dx.doi.org/10.1017/S0013091506001532[WoS][Crossref]
  • [14] Xiao J., Nieto J.J., Variational approach to some damped Dirichlet nonlinear impulsive differential equations, J. Franklin Inst., 2011, 48(2), 369–377 http://dx.doi.org/10.1016/j.jfranklin.2010.12.003[WoS][Crossref]
  • [15] Zavalishchin S.T., Sesekin A.N., Dynamic Impulse Systems, Math. Appl., 394, Kluwer, Dordrecht, 1997
  • [16] Zhang H., Li Z., Variational approach to impulsive differential equations with periodic boundary conditions, Nonlinear Anal. Real World Appl., 2010, 11(1), 67–78 http://dx.doi.org/10.1016/j.nonrwa.2008.10.016[Crossref]
  • [17] Zhang Z., Yuan R., An application of variational methods to Dirichlet boundary value problem with impulses, Nonlinear Anal. Real World Appl., 2010, 11(1), 155–162 http://dx.doi.org/10.1016/j.nonrwa.2008.10.044[Crossref]

Typ dokumentu

Bibliografia

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bwmeta1.element.doi-10_2478_s11533-012-0084-9
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