Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies

Elmostafa Bendib; Mustapha Khiddi

Applications of Mathematics (2025)

  • Issue: 3, page 441-456
  • ISSN: 0862-7940

Abstract

top
We investigate a class of Kirchhoff-type equations characterized by critical growth within Orlicz-Sobolev spaces. The main result establishes the existence of infinitely many solutions with negative energy. Using an adapted concentration-compactness principle and advanced variational methods, we overcome key challenges such as non-compactness and non-differentiability to the associated functionals. This work extends existing results to more general functional spaces, offering new insights into nonlocal nonlinear equations.

How to cite

top

Bendib, Elmostafa, and Khiddi, Mustapha. "Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies." Applications of Mathematics (2025): 441-456. <http://eudml.org/doc/299995>.

@article{Bendib2025,
abstract = {We investigate a class of Kirchhoff-type equations characterized by critical growth within Orlicz-Sobolev spaces. The main result establishes the existence of infinitely many solutions with negative energy. Using an adapted concentration-compactness principle and advanced variational methods, we overcome key challenges such as non-compactness and non-differentiability to the associated functionals. This work extends existing results to more general functional spaces, offering new insights into nonlocal nonlinear equations.},
author = {Bendib, Elmostafa, Khiddi, Mustapha},
journal = {Applications of Mathematics},
keywords = {Kirchhoff type problem; Orlicz-Sobolev space; $\Delta _\{2\}$-condition},
language = {eng},
number = {3},
pages = {441-456},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies},
url = {http://eudml.org/doc/299995},
year = {2025},
}

TY - JOUR
AU - Bendib, Elmostafa
AU - Khiddi, Mustapha
TI - Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 3
SP - 441
EP - 456
AB - We investigate a class of Kirchhoff-type equations characterized by critical growth within Orlicz-Sobolev spaces. The main result establishes the existence of infinitely many solutions with negative energy. Using an adapted concentration-compactness principle and advanced variational methods, we overcome key challenges such as non-compactness and non-differentiability to the associated functionals. This work extends existing results to more general functional spaces, offering new insights into nonlocal nonlinear equations.
LA - eng
KW - Kirchhoff type problem; Orlicz-Sobolev space; $\Delta _{2}$-condition
UR - http://eudml.org/doc/299995
ER -

References

top
  1. Benci, V., Fortunato, D., Pisani, L., 10.1142/S0129055X98000100, Rev. Math. Phys. 10 (1998), 315-344. (1998) Zbl0921.35177MR1626832DOI10.1142/S0129055X98000100
  2. Dacorogna, B., 10.1142/q0451, World Scientific, Singapore (2025). (2025) Zbl1548.49001MR4810953DOI10.1142/q0451
  3. Donaldson, T., 10.1016/0022-0396(71)90009-X, J. Differ. Equations 10 (1971), 507-528. (1971) Zbl0218.35028MR0298472DOI10.1016/0022-0396(71)90009-X
  4. Donaldson, T. K., Trudinger, N. S., 10.1016/0022-1236(71)90018-8, J. Funct. Anal. 8 (1971), 52-75. (1971) Zbl0216.15702MR0301500DOI10.1016/0022-1236(71)90018-8
  5. Fukagai, N., Ito, M., Narukawa, K., 10.1619/fesi.49.235, Funkc. Ekvacioj, Ser. Int. 49 (2006), 235-267. (2006) Zbl1387.35405MR2271234DOI10.1619/fesi.49.235
  6. Fukagai, N., Ito, M., Narukawa, K., 10.1017/S0308210507000765, Proc. R. Soc. Edinb., Sect. A, Math. 139 (2009), 73-106. (2009) Zbl1169.35017MR2487034DOI10.1017/S0308210507000765
  7. Fukagai, N., Narukawa, K., 10.32917/hmj/1206127823, Hiroshima Math. J. 25 (1995), 19-41. (1995) Zbl0836.35112MR1322600DOI10.32917/hmj/1206127823
  8. Fukagai, N., Narukawa, K., 10.1007/s10231-006-0018-x, Ann. Mat. Pura Appl. (4) 186 (2007), 539-564. (2007) Zbl1223.35132MR2317653DOI10.1007/s10231-006-0018-x
  9. Azorero, J. Garcia, Alonso, I. Peral, 10.1090/S0002-9947-1991-1083144-2, Trans. Am. Math. Soc. 323 (1991), 877-895. (1991) Zbl0729.35051MR1083144DOI10.1090/S0002-9947-1991-1083144-2
  10. Hssini, E. M., Tsouli, N., Haddaoui, M., 10.1515/apam-2016-0065, Adv. Pure Appl. Math. 8 (2017), 197-208. (2017) Zbl1381.35041MR3667067DOI10.1515/apam-2016-0065
  11. Kavian, O., Introduction à la théorie des points critiques et applications aux problèmes elliptiques, Mathématiques & Applications (Berlin) 13. Springer, Paris (1993), French. (1993) Zbl0797.58005MR1276944
  12. Khiddi, M., Sbai, S. M., 10.1080/17476933.2019.1627527, Complex Var. Elliptic Equ. 65 (2020), 368-380. (2020) Zbl1430.35255MR4052692DOI10.1080/17476933.2019.1627527
  13. Lions, P.-L., 10.4171/RMI/6, Rev. Mat. Iberoam. 1 (1985), 145-201. (1985) Zbl0704.49005MR0834360DOI10.4171/RMI/6
  14. Mihăilescu, M., Repovš, D., 10.1016/j.amc.2011.01.050, Appl. Math. Comput. 217 (2011), 6624-6632. (2011) Zbl1211.35117MR2773249DOI10.1016/j.amc.2011.01.050
  15. Tsouli, N., Haddaoui, M., Hssini, E. M., Multiple solutions for a critical p ( x ) -Kirchhoff type equations, Bol. Soc. Parana Mat. (3) 38 (2020), 197-211. (2020) Zbl1431.35014MR3912304

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.