On variational impulsive boundary value problems

Marek Galewski

Open Mathematics (2012)

  • Volume: 10, Issue: 6, page 1969-1980
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Marek Galewski. "On variational impulsive boundary value problems." Open Mathematics 10.6 (2012): 1969-1980. <http://eudml.org/doc/269644>.

@article{MarekGalewski2012,
abstract = {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.},
author = {Marek Galewski},
journal = {Open Mathematics},
keywords = {Variational method; Critical point; Dirichlet problem; Impulsive conditions; Continuous dependence on parameters; variational method; critical point; impulsive conditions; continuous dependence on parameters},
language = {eng},
number = {6},
pages = {1969-1980},
title = {On variational impulsive boundary value problems},
url = {http://eudml.org/doc/269644},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Marek Galewski
TI - On variational impulsive boundary value problems
JO - Open Mathematics
PY - 2012
VL - 10
IS - 6
SP - 1969
EP - 1980
AB - 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.
LA - eng
KW - Variational method; Critical point; Dirichlet problem; Impulsive conditions; Continuous dependence on parameters; variational method; critical point; impulsive conditions; continuous dependence on parameters
UR - http://eudml.org/doc/269644
ER -

References

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  1. [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. [2] Chen H., Li J., Variational approach to impulsive differential equations with Dirichlet boundary conditions, Bound. Value Probl., 2010, #325415 [WoS][Crossref] 
  3. [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. [4] Idczak D., Rogowski A., On a generalization of Krasnoselskii’s theorem, J. Aust. Math. Soc., 2002, 72(3), 389–394 Zbl1030.47044
  5. [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. [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] Zbl0719.34002
  7. [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 Zbl1031.49002
  8. [8] Mawhin J., Problèmes de Dirichlet Variationnels non Linéaires, Sem. Math. Sup., 104, Presses de l’Université de Montréal, Montréal, 1987 
  9. [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. [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. [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. [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. [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] Zbl1163.34015
  14. [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. [15] Zavalishchin S.T., Sesekin A.N., Dynamic Impulse Systems, Math. Appl., 394, Kluwer, Dordrecht, 1997 Zbl0880.46031
  16. [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. [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] 

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