Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions

Sahbi Boussandel

Applications of Mathematics (2018)

  • Volume: 63, Issue: 5, page 523-539
  • ISSN: 0862-7940

Abstract

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The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet p -Laplace operator.

How to cite

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Boussandel, Sahbi. "Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions." Applications of Mathematics 63.5 (2018): 523-539. <http://eudml.org/doc/294778>.

@article{Boussandel2018,
abstract = {The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet $p$-Laplace operator.},
author = {Boussandel, Sahbi},
journal = {Applications of Mathematics},
keywords = {existence of solutions; anti-periodic; monotone operator; maximal monotone operator; Schaefer fixed-point theorem; monotonicity method; diffusion equation},
language = {eng},
number = {5},
pages = {523-539},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions},
url = {http://eudml.org/doc/294778},
volume = {63},
year = {2018},
}

TY - JOUR
AU - Boussandel, Sahbi
TI - Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 5
SP - 523
EP - 539
AB - The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet $p$-Laplace operator.
LA - eng
KW - existence of solutions; anti-periodic; monotone operator; maximal monotone operator; Schaefer fixed-point theorem; monotonicity method; diffusion equation
UR - http://eudml.org/doc/294778
ER -

References

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  1. Aftabizadeh, A. R., Aizicovici, S., Pavel, N. H., 10.1016/0022-247X(92)90345-E, J. Math. Anal. Appl. 171 (1992), 301-320. (1992) Zbl0767.34047MR1194081DOI10.1016/0022-247X(92)90345-E
  2. Aizicovici, S., McKibben, M., Reich, S., 10.1016/S0362-546X(99)00192-3, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 43 (2001), 233-251. (2001) Zbl0977.34061MR1790104DOI10.1016/S0362-546X(99)00192-3
  3. Aizicovici, S., Pavel, N. H., 10.1016/0022-1236(91)90046-8, J. Funct. Anal. 99 (1991), 387-408. (1991) Zbl0743.34067MR1121619DOI10.1016/0022-1236(91)90046-8
  4. Boussandel, S., 10.21136/AM.2018.0233-17, Appl. Math., Praha 63 (2018), 423-437. (2018) Zbl06945740MR3842961DOI10.21136/AM.2018.0233-17
  5. Browder, F. E., Petryshyn, W. V., 10.1090/S0002-9904-1966-11544-6, Bull. Am. Math. Soc. 72 (1966), 571-575. (1966) Zbl0138.08202MR0190745DOI10.1090/S0002-9904-1966-11544-6
  6. Chen, Y., 10.1016/j.jmaa.2005.08.001, J. Math. Anal. Appl. 315 (2006), 337-348. (2006) Zbl1100.34046MR2196551DOI10.1016/j.jmaa.2005.08.001
  7. Chen, Y., Cho, Y. J., Jung, J. S., 10.1016/j.mcm.2003.06.007, Math. Comput. Modelling 40 (2004), 1123-1130. (2004) Zbl1074.34058MR2113840DOI10.1016/j.mcm.2003.06.007
  8. Chen, Y., Nieto, J. J., O'Regan, D., 10.1016/j.mcm.2006.12.006, Math. Comput. Modelling 46 (2007), 1183-1190. (2007) Zbl1142.34313MR2376702DOI10.1016/j.mcm.2006.12.006
  9. Chen, Y., Nieto, J. J., O'Regan, D., 10.1016/j.aml.2010.10.010, Appl. Math. Lett. 24 (2011), 302-307. (2011) Zbl1215.34069MR2741034DOI10.1016/j.aml.2010.10.010
  10. Chen, Y., O'Regan, D., Agarwal, R. P., 10.1016/j.aml.2010.06.022, Appl. Math. Lett. 23 (2010), 1320-1325. (2010) Zbl1208.34098MR2718504DOI10.1016/j.aml.2010.06.022
  11. Chen, Y., O'Regan, D., Agarwal, R. P., 10.1007/s12190-010-0463-y, J. Appl. Math. Comput. 38 (2012), 63-70. (2012) Zbl1302.34097MR2886666DOI10.1007/s12190-010-0463-y
  12. Chen, Y., Wang, X., Xu, H., 10.1016/S0022-247X(02)00288-3, J. Math. Anal. Appl. 273 (2002), 627-636. (2002) Zbl1055.34113MR1932511DOI10.1016/S0022-247X(02)00288-3
  13. Drábek, P., Milota, J., 10.1007/978-3-0348-0387-8, Birkhäuser Advanced Texts. Basler Lehrbücher, Birkhäuser, Basel (2007). (2007) Zbl1176.35002MR2323436DOI10.1007/978-3-0348-0387-8
  14. Gajewski, H., Gröger, K., Zacharias, K., 10.1002/mana.19750672207, Mathematische Lehrbücher und Monographien, II. Abteilung, Mathematische Monographien 38, Akademie, Berlin German (1974). (1974) Zbl0289.47029MR0636412DOI10.1002/mana.19750672207
  15. Gilbarg, D., Trudinger, N. S., 10.1007/978-3-642-61798-0, Classics in Mathematic, Springer, Berlin (2001). (2001) Zbl1042.35002MR1814364DOI10.1007/978-3-642-61798-0
  16. Haraux, A., 10.1007/BF01171760, Manuscr. Math. 63 (1989), 479-505. (1989) Zbl0684.35010MR0991267DOI10.1007/BF01171760
  17. Liu, Y., Liu, X., New existence results of anti-periodic solutions of nonlinear impulsive functional differential equations, Math. Bohem. 138 (2013), 337-360. (2013) Zbl1289.34168MR3231091
  18. Nakao, M., 10.1006/jmaa.1996.0465, J. Math. Anal. Appl. 204 (1996), 754-764. (1996) Zbl0873.35051MR1422770DOI10.1006/jmaa.1996.0465
  19. Okochi, H., 10.2969/jmsj/04030541, J. Math. Soc. Japan 40 (1988), 541-553. (1988) Zbl0679.35046MR0945351DOI10.2969/jmsj/04030541
  20. Okochi, H., 10.1016/0022-1236(90)90143-9, J. Funct. Anal. 91 (1990), 246-258. (1990) Zbl0735.35071MR1058971DOI10.1016/0022-1236(90)90143-9
  21. Okochi, H., 10.1016/0362-546X(90)90105-P, Nonlinear Anal., Theory Methods Appl. 14 (1990), 771-783. (1990) Zbl0715.35091MR1049120DOI10.1016/0362-546X(90)90105-P
  22. Simon, J., 10.1007/BF01762360, Ann. Mat. Pura Appl., IV. Ser. 146 (1987), 65-96. (1987) Zbl0629.46031MR0916688DOI10.1007/BF01762360
  23. Souplet, P., An optimal uniqueness condition for the antiperiodic solutions of parabolic evolution equations, C. R. Acad. Sci., Paris, Sér. I 319 (1994), 1037-1041 French. (1994) Zbl0809.35036MR1305673
  24. Souplet, P., 10.1016/S0362-546X(97)00477-X, Nonlinear Anal., Theory Methods Appl. 32 (1998), 279-286. (1998) Zbl0892.35078MR1491628DOI10.1016/S0362-546X(97)00477-X
  25. Tian, Y., Henderson, J., 10.1002/mana.201200110, Math. Nachr. 286 (2013), 1537-1547. (2013) Zbl1283.34016MR3119700DOI10.1002/mana.201200110
  26. Wu, R., 10.1016/j.aml.2010.04.022, Appl. Math. Lett. 23 (2010), 984-987. (2010) Zbl1202.34081MR2659124DOI10.1016/j.aml.2010.04.022
  27. Wu, R., Cong, F., Li, Y., 10.1016/j.aml.2010.12.031, Appl. Math. Lett. 23 (2011), 860-863. (2011) Zbl1223.34064MR2776149DOI10.1016/j.aml.2010.12.031
  28. Zeidler, E., 10.1007/978-1-4612-0985-0, Springer, New York (1990). (1990) Zbl0684.47028MR1033497DOI10.1007/978-1-4612-0985-0
  29. Zhenhai, L., 10.1016/j.jfa.2009.11.018, J. Funct. Anal. 258 (2010), 2026-2033. (2010) Zbl1184.35184MR2578462DOI10.1016/j.jfa.2009.11.018

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