Nonlinear Functional Analysis and Applications

  • 제27권3호
  • /
  • Pages.649-662
  • /
  • 2022
  • /
  • 1229-1595(pISSN)
  • /
  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
권호 표지
DOI QR코드

DOI QR Code

STUDY OF A CRITICAL 𝚽-KIRCHHOFF TYPE EQUATIONS IN ORLICZ-SOBOLEV SPACES

  • Haddaoui, Mustapha (ROALI Team, LMIMA Laboratory, FST-Erachidia, Moulay Ismail University of Mekns) ;
  • Tsouli, Najib (LAMAO Laboratory, Department of Mathematics, Faculty of Science, University Mohammed I) ;
  • Zaki, Ayoub (LAMAO Laboratory, Department of Mathematics, Faculty of Science, University Mohammed I)
  • 투고 : 2021.12.02
  • 심사 : 2022.03.27
  • 발행 : 2022.09.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper is concerned with the existence of solutions for a class of 𝚽-Kirchhoff type equations with critical exponent in Orlicz-Sobolev spaces. Our technical approach is based on variational methods.

키워드

참고문헌

  1. A. Adams and J.F. Fournier, Sobolev spaces, 2nd ed, Academic Press, (2003).
  2. A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381. https://doi.org/10.1016/0022-1236(73)90051-7
  3. G. Bonano, G.M. Bisci and V. Radulescu, Quasilinear elliptic non-homogeneous Dirichlet problems through Orlicz-Sobolev spaces, Nonlinear Anal., 75 (2012), 4441-4456. https://doi.org/10.1016/j.na.2011.12.016
  4. H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functinals, Proc. Amer. Math. Soc., 88 (1983), 486-490. https://doi.org/10.1090/S0002-9939-1983-0699419-3
  5. J. Chabrowski, Weak covergence methods for semilinear elliptic equations, World Scientific Publishing Company, 1999.
  6. Ph. Clement, M. Garcia-Huidobro, R. Manasevich and K. Schmitt, Mountain pass type solutions for quasilinear elliptic equations, Calc. Var., 11 (2000), 33-62. https://doi.org/10.1007/s005260050002
  7. T.K. Donaldson, Nonlinear elliptic boundary value problems in Orlicz-Sobolev spaces, J. Diff. Equ., 10 (1971), 507-528. https://doi.org/10.1016/0022-0396(71)90009-X
  8. T.K. Donaldson and N.S. Trudinger, Orlicz-Sobolev spaces and imbedding theorems, J. Funct. Anal., 8 (1971), 52-75. https://doi.org/10.1016/0022-1236(71)90018-8
  9. A.R. Elamrouss and F. Kissi, Multiplicity of solutions for a general p(x)-Laplacian Dirichlet problem , Arab J. Math. Sci., 19(2) (2013), 205-216.
  10. N. Fukagai, M. Ito and K. Narukawa, Positive solutions of quasilinear elliptic equations with critical Orlicz-Sobolev nonlinearity on ℝN, Funkcialaj Ekvacioj, 49 (2006), 235-267. https://doi.org/10.1619/fesi.49.235
  11. N. Fukagai, M. Ito and K. Narukawa, Quasilinear elliptic equations with slowly growing principal part and critical Orlicz-Sobolev nonlinear term, Proc. R. S. Edinburgh, 139(A) (2009), 73-106. https://doi.org/10.1017/S0308210507000765
  12. N. Fukagai and K. Narukawa, On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems, Annali di Matematica, 186 (2007), 539-564. https://doi.org/10.1007/s10231-006-0018-x
  13. A. Hamydy, M. Massar and N. Tsouli, Existence of solutions for p-Kirchhoff type problems with critical exponent, Elect. J. Diff. Equ., 2011(105) (2011), 1-8.
  14. EL M. Hssini, N. Tsouli and M. Haddaoui, Existence and multiplicity solutions for (p(x), q(x))-Kirchhoff type systems, Le Mate., LXXI (2016), 75-88.
  15. EL M. Hssini, N. Tsouli and M. Haddaoui, Existence results for a Kirchhoff type equation in Orlicz-Sobolev spaces, Adv. Pure Appl. Math., 8(3) (2017), 197-208.
  16. M. Mihailescu and V. Radulescu, Existence and multiplicity of solutions for a quasilinear nonhomogeneous problems: An Orlicz-Sobolev space setting, J. Math. Anal. Appl., 330 (2007), 416-432. https://doi.org/10.1016/j.jmaa.2006.07.082
  17. M. Mihailescu and D. Repovs, Multiple solutions for a nonlinear and non-homogeneous problems in Orlicz-Sobolev spaces, Appl. Math. Comput., 217 (2011), 6624-6632.
  18. R. O'Neill; Fractional integration in Orlicz spaces, Trans. Amer. Math. Soc., 115 (1965), 300-328. https://doi.org/10.2307/1994271
  19. A. Ourraoui, On a p-Kirchhoff problem involving a critical nonlinearity, C. R. Acad. Sci. Paris, Ser. I. 1352(2014), 295-298. https://doi.org/10.1016/j.crma.2014.01.015
  20. P.H. Rabinowitz, Minimax methods in critical point theory with applications to diferential equations. CBMS Reg. Conf. Sries in Math., 65 (1984).
  21. J.A. Santos, Multiplicity of solution for quasilinear equation involving critical Orlicz-Sobolev Nonlinear terms, Ele. J. Diff. Equ., 2013(249) (2013), 1-13. https://doi.org/10.1186/1687-1847-2013-1
  22. N. Tsouli , M. Haddaoui and EL M. Hssini, Multiplicity results for a Kirchhoff type equations in Orlicz-Sobolev spaces, Nonlinear Studies, CSP - Cambridge, UK; I and S - Florida, USA, 26(3) (2019), 637-652.
  23. N. Tsouli , M. Haddaoui and EL M. Hssini, Multiple Solutions for a Critical p(x)-Kirchhoff Type Equations, Bol. Soc. Paran. Mat. (3s.) 38(4) (2020), 197-211.
  24. M. Willem, Minimax theorems, Birkhauser, 1996.
  25. W. Zhihui and W. Xinmin, A multiplicity result for quasilinear elliptic equations involving critical Sobolev exponents. Nonlinear Anal., 18 (1992), 559-567. https://doi.org/10.1016/0362-546X(92)90210-6