Existence of multiple solutions for a nonhomogeneous p-Laplacian elliptic equation with critical Sobolev-Hardy exponent

  • Atika Matallah Higher School of Management of Tlemcen
  • Sara Litimein University of Sidi Bel Abb`es
  • Sofiane Messirdi Université de Mostaganem
Keywords: Variational methods, critical Hardy-Sobolev exponent, Nehari manifold, p-Laplacain equations.

Abstract

This paper is concerned with the existence of multiple nontrivial solutions for nonhomogeneous p-Laplacain elliptic problems involving the critical Hardy-Sobolev exponent. The method used here is based on the Nehari manifold.

Downloads

Download data is not yet available.

Author Biography

Sofiane Messirdi, Université de Mostaganem

Département de mathématiques et informatique faculté des sciences exactes université de Mostaganem Algérie

References

Assuncao, R., Carriao, P., Miyagaki, O. Subcritical perturbations of a singular quasilinear elliptic equation involving the critical Hardy-Sobolev exponent. Nonlinear Anal. 66, 1351-1364 (2007). https://doi.org/10.1016/j.na.2006.01.027

Bouchekif, M., Matallah, A. Multiple positive solutions for elliptic equations involving a concave term and critical Sobolev-Hardy exponent. Appl. Math. Lett. 22, 268-275 (2009). https://doi.org/10.1016/j.aml.2008.03.024

Brezis, H., Lieb, E. A Relation Between Point Convergence of Functions and Convergence of Functionals. Proc. Amer. Math. Soc. 88, 486-490 (1983). https://doi.org/10.1090/S0002-9939-1983-0699419-3

Caffarelli, L., Kohn, R., Nirenberg, L. First order interpolation inequality with weights. Compos. Math. 53, 259-275 (1984).

Ekeland, I. On the variational principle. J. Math. Anal. Appl. 47, 324-354 (1974). https://doi.org/10.1016/0022-247X(74)90025-0

Filippucci, R., Pucci, P., Robert, F. On a p-Laplace equation with multiple critical nonlinearities. J. Math. Pures Appl. 91, 156-177 (2009). https://doi.org/10.1016/j.matpur.2008.09.008

Garcia Azorero, J. P., Peral Alonso, I. Hardy Inequalities and Some Critical Elliptic and Parabolic Problems. J. of Differential Equations. 144, 441-476 (1998). https://doi.org/10.1006/jdeq.1997.3375

Ghoussoub, N., Yuan, C. Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents. Trans. Amer. Math. Soc. 352, 5703-5743 (2000). https://doi.org/10.1090/S0002-9947-00-02560-5

Kang, D. S. On the quasilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy terms. Nonlinear Anal. 68, 1973-1985 (2008). https://doi.org/10.1016/j.na.2007.01.024

Sang, Y. Guo, S. Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent. Journal of Inequalities and Applications. (2017). https://doi.org/10.1186/s13660-017-1492-y

Secchi, S., Smets, D., Willem, M. Remarks on a Hardy-Sobolev inequality. C.R. Acad. Sci. Paris. 336, 811-815 (2003). https://doi.org/10.1016/S1631-073X(03)00202-4

Liang, S. H., Zhang, J. H. Multiplicity of solutions for a class of quasilinear elliptic equation involving the critical Sobolev and Hardy exponents. Nonlinear Differ. Equ. Appl. 17, 55-67 (2010). https://doi.org/10.1007/s00030-009-0039-4

Tarantello, G. On nonhomogeneous elliptic equations involving critical Sobolev exponent. Ann. Inst. Henri Poincare 9, 281-304 (1992). https://doi.org/10.1016/S0294-1449(16)30238-4

Published
2022-01-24
Section
Articles