Existence of multiple solutions for a nonhomogeneous p-Laplacian elliptic equation with critical Sobolev-Hardy exponent
DOI:
https://doi.org/10.5269/bspm.46206Keywords:
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.
References
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12. 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
13. 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
2. 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
3. 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
4. Caffarelli, L., Kohn, R., Nirenberg, L. First order interpolation inequality with weights. Compos. Math. 53, 259-275 (1984).
5. Ekeland, I. On the variational principle. J. Math. Anal. Appl. 47, 324-354 (1974). https://doi.org/10.1016/0022-247X(74)90025-0
6. 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
7. 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
8. 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
9. 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
10. 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
11. 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
12. 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
13. 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
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2022-01-24
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