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Existence of solutions for a nonlinear problem at resonance

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this work, we are interested at the existence of nontrivial solutions for a nonlinear elliptic problem with resonance part and nonlinear boundary conditions. Our approach is variational and is based on the well-known Landesman-Laser-type conditions.
Wydawca
Rocznik
Strony
482--489
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
  • University Moulay Ismail, FST Errachidia, LAMIMA Laboratory, ROALI Team, Errachidia, Morocco
  • University Mohamed I, FS Oujda, ANOL Laboratory, Oujda, Morocco
  • University Mohamed I, FS Oujda, ANOL Laboratory, Oujda, Morocco
autor
  • University Mohamed I, FS Oujda, ANOL Laboratory, Oujda, Morocco
Bibliografia
  • [1] A. Anane, Etude des valeurs propres et de la résonance pour laopérateur p-Laplacien (french), R. Ac. Sc. Paris. 305 (1987), 725–728.
  • [2] A. Anane, O. Chakrone, B. Karim, and A. Zerouli, Existence of solution for a resonant Steklov problem, Bol. Soc. Paran. Mat. (3s.) 27 (2009), no. 1, 87–90, DOI: https://doi.org/10.5269/bspm.v27i1.9070.
  • [3] A. Anane and J. P. Gossez, Strongly nonlinear elliptic problems near resonance a variational approach, Comm. Partial Diff. Eqns. 15 (1990), no. 8, 1141–1159, DOI: https://doi.org/10.1080/03605309908820717.
  • [4] P. Drabek and S. B. Robinson, Resonance problems for the p-Laplacian, J. Funct. Anal. 169 (1999), no. 1, 189–200, DOI: https://doi.org/10.1006/jfan.1999.3501.
  • [5] S. Liu and M. Squassina, On the existence of solutions to a fourth-order quasilinear resonant problem, Abstr. Appl. Anal. 7 (2002), 347809, DOI: https://doi.org/10.1155/S1085337502000805.
  • [6] L. Xu, Multiplicity results for fourth-order boundary-value problem at resonance with variable coefficients, Electron. J. Differ. Equ. 2008 (2008), no. 100, 1–8.
  • [7] E. M. Hssini, M. Massar, M. Talbi, and N. Tsouli, Existence of solutions for a fourth order problem at resonance, Bol. Soc. Paran. Mat. (3s.) 32 (2014), no. 2, 133–142, DOI: https://doi.org/10.5269/bspm.v32i2.18216.
  • [8] M. Massar, E. M. Hssini, and N. Tsouli, Existence and multiplicity of solutions for class of Navier boundary p-biharmonic problem near resonance, Bol. Soc. Paran. Mat. (3s.), 32 (2014), no. 2, 83–93, DOI: https://doi.org/10.5269/bspm.v32i2.17522.
  • [9] S. Z. Song and C. L. Tang, Resonance problems for the p-Laplacian with a nonlinear boundary condition, Nonlinear Anal. 64 (2006), no. 9, 2007–2021, DOI: https://doi.org/10.1016/j.na.2005.07.035.
  • [10] M. Haddaoui, H. Lebrimchi, and N. Tsouli, A resonance problem for p-Laplacian with mixed boundary conditions. Bol. Soc. Paran. Mat. (2021), 1–9, DOI: 10.5269/bspm.52640.
  • [11] N. Tsouli, O. Chakrone, O. Darhouche, and M. Rahmani, Nonlinear eigenvalue problem for the p-Laplacian, Commun. Math. Anal. 20 (2017), 69–82.
  • [12] S. G. Deng, Positive solutions for Robin problem involving the ( )p x -Laplacian, J. Math. Anal. Appl. 360 (2009), no. 2, 548–560, DOI: https://doi.org/10.1016/j.jmaa.2009.06.032.
  • [13] P. H. Rabinowitz, Some minimax theorems and applications to partial differential equations, in: Lamberto Cesari, Rangachari Kannan, Hans F. Weinberger (eds), Nonlinear Analysis, Academic Press, New York, 1978, pp . 161–177, DOI: https://doi.org/10.1016/B978-0-12-165550-1.50016-1.
  • [14] M. Talbi and N. Tsouli, On the spectrum of the weighted p-biharmonic operator with weight, Miditerr. J. Math. 4 (2007), no. 1, 73–86, DOI: https://doi.org/10.1007/s00009-007-0104-3.
  • [15] C. O. Alves, P. C. Carriao, and O. H. Miyagaki, Multiple solutions for a problem with resonance involving the p-Laplacian, Abstr. Appl. Anal. 3 (1998), 315492, DOI: https://doi.org/10.1155/S1085337598000517.
  • [16] S. Ahmad, A. C. Lazer, and J. L. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), no. 10, pp. 933–944, https://www.jstor.org/stable/24891061.
  • [17] D. Arcoya and L. Orsina, Landesman-Lazer conditions and quasilinear elliptic equations, Nonlinear Anal. 28 (1997), no. 10, 1623–1632, DOI: https://doi.org/10.1016/S0362-546X(96)00022-3.
  • [18] Q. A. Ngo and H. Q. Toan, Existence of solution for a resonant Problem Under Landesman-Lazer conditions, Electron. J. Differential Equations 2008 (2008), no. 98, 1–10.
  • [19] N. T. Vu,Mountain pass solutions and non-uniformly elliptic equations, Vietnam J. Math. 33 (2005), no. 4, 391–408.
  • [20] N. Mavinga, Generalized eigenproblem and nonlinear elliptic equations with nonlinear boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 142 (2012), 137–153, DOI: https://doi.org/10.1017/S0308210510000065.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6339619b-04e3-469c-9b56-9b8f7a32621a
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