DOI QR코드

DOI QR Code

EXISTENCE RESULTS FOR p-LAPLACIAN PROBLEMS INVOLVING SINGULAR CYLINDRICAL POTENTIAL

  • Received : 2023.03.09
  • Accepted : 2023.08.31
  • Published : 2023.12.15

Abstract

In this paper, we establish the existence of at least two distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold.

Keywords

References

  1. A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal., 122 (1994), 519-543. https://doi.org/10.1006/jfan.1994.1078
  2. R.B. Assuncao, O.H. Miyagaki, L.C. Paes-Leme and B.M. Rodrigues, Existence and Multiplicity Results for an Elliptic Problem Involving Cylindrical Weights and a Homogeneous Terms µ, Mediterranean J. Math., 2019 (2019), 1-10.
  3. M. Badiale, V. Bergio and S. Rolando, A nonlinear elliptic equation with singular potential and applications to nonlinear field equations, J. Eur. Math. Soc., 9 (2007), 355-381. https://doi.org/10.4171/jems/83
  4. M. Badiale, M, Guida and S. Rolando, Elliptic equations with decaying cylindrical potentials and power-type nonlinearities, Adv. Diff. Equ., 12 (2007) 1321-1362.
  5. M. Badiale and G. Tarantello, A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics, Arch. Ration. Mech. Anal., 163 (2002), 252-293. https://doi.org/10.1007/s002050200201
  6. M. Bhakta and K. Sandeep, Hardy-Sobolev-Maz'ya type equations in bounded domains, J. Diffe. Equ., 247 (2009), 119-139. https://doi.org/10.1016/j.jde.2008.12.011
  7. K.J. Brown and Y. Zhang, The Nehari manifold for a semilinear elliptic equation with a signchanging weight function, J. Diff. Equ., 193 (2003), 481-499. https://doi.org/10.1016/S0022-0396(03)00121-9
  8. D.M. Cao, S.J. Peng and S.S. Yan, Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth, J. Funct. Anal., 262 (2012), 2861-2902. https://doi.org/10.1016/j.jfa.2012.01.006
  9. P. Drabek, A. Kufner and F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singularities, Walter de Gruyter Series in Nonlinear Analysis and Applications, 5, New York, 1997.
  10. D.G. de Figueiredo, J.P. Gossez and P. Ubilla, Local superlinearity and sublinearity for indefinite semilinear elliptic problemsm, J. Funct. Anal., 199 (2003), 452-467. https://doi.org/10.1016/S0022-1236(02)00060-5
  11. R. Filippucci, P. Pucci and F. Robert, On a p-Laplace equation with multiple critical nonlinearities, J. Math. Pure Appl., 91 (2009), 156-177. https://doi.org/10.1016/j.matpur.2008.09.008
  12. M. Gazzini, A. Ambrosetti and R. Musina, Nonlinear elliptic problems related to some integral inequalities, http://digitallibrary.sissa.it/retrieve/4320/PhDThesisGazzini.pdf.
  13. M. Gazzini and R. Mussina, On a Sobolev type inequality related to the weighted p-Laplace operator, J. Math. Anal. Appl., 352 (2009), 99-111. https://doi.org/10.1016/j.jmaa.2008.06.021
  14. Y.Y. Li, Q.Q. Guo and P.C. Niu, Global compactness results for quasilinear elliptic problems with combined critical Sobolev-Hardy terms, Nonlinear Anal., 74 (2011), 1445-1464. https://doi.org/10.1016/j.na.2010.10.018
  15. R. Musina, Ground state solutions of a critical problem involving cylindrical weights, Nonlinear Anal., 68 (2008), 3972-3986. https://doi.org/10.1016/j.na.2007.04.034
  16. G. Tarantello, Multiplicity results for an inhomogeneous Neumann problem critical exponent, Manuscripta Math., 81 (1993), 57-78. https://doi.org/10.1007/BF02567844
  17. T.F. Wu, Multiplicity results for a semilinear elliptic equation involving sign-changing weight function, Rocky Mountain J. Math., 39(3) (2009), 995-1011. https://doi.org/10.1216/RMJ-2009-39-3-995
  18. B.J. Xuan, Multiple solutions to p-Laplacian equation with singularity and cylindrical symmetry, Nonlinear Anal., 55 (2003), 217-232. https://doi.org/10.1016/S0362-546X(03)00224-4
  19. X. Zhang and C. Yuan, Twin of positive solutions for four-point singular boundary value problems with p-Laplacian operator, Nonlinear Funct. anal. appl., 14(2)(2009), 167-180. https://doi.org/10.1155/2009/103276