Existence of solutions for singular elliptic problems with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent
DOI:
https://doi.org/10.58997/ejde.2023.54Abstract
In this article, we consider a singular elliptic problem with singular nonlinearities and critical Caffarelli-Kohn-Nirenberg exponent. By using variational methods and Palais-Smale condition, we show the existence of at least two nontrivial solutions. The result depends crucially on the parameters \(a,b,N,\beta,\gamma,\lambda,\mu\).
For more information see https://ejde.math.txstate.edu/Volumes/2023/54/abstr.html
References
M. Ali, J. A. Iaia; Existence and nonexistence for singular sublinear problems on exterior domains. Electronic Journal of Differential Equations, 2021 (2021) no. 03, 1-17.
A. Ambrosetti, P. H. Rabinowitz; Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, (1973), 349-381.
H. Brezis, E. Lieb; A Relation Between Point convergence of Functions and convergence of Functional, Proc. Amer. Math. Soc. 88 (1983), 486-490.
M. Bouchekif, A. Matallah; On singular nonhomogeneous elliptic equations involving critical Caffarelli-Kohn-Nirenberg exponent, Ric. Mat. 58 (2009), 207-218.
L. Caffarelli, R. Kohn, L. Nirenberg; First order interpolation inequality with weights, Compos. Math. 53 (1984), 259-275.
K. Chou, C. Chu; On the best constant for a weighted Sobolev-Hardy inequality, J. Lond. Math. Soc, 2 (1993), 137-151.
R. Dautray, J. L. Lions; Physical Origins and Classical Methods in Mathematical Analysis and Numerical Methods for Science and Technology, Springer, Berlin (1990).
I. Ekeland; On the variational principle, J. Math. Anal. Appl. 47 (1974) 323-353.
D. Kang, G. Li, S. Peng; Positive solutions and critical dimensions for the elliptic problems involving the Caffarelli-Kohn-Nirenberg inequalities, J. Jilin. Univ. Sci. 46 (2008) 423–427.
R. Q. Liu, C. Lei Tang, J. F. Liao, X. Ping Wu;
Positive solutions of Kirchhoff type problem with singular and critical nonlinearities in dimension four, Communications on pure and applied analysis, 15(2016) 1841-1856.
G. Tarantello; On nonhomogeneous elliptic equations involving critical Sobolev exponent, Ann. Inst. Henri PoincarŽe, 9 (1992) 281-304.
B. J. Xuan ; Multiple solutions to p-Laplacian equation with singularity and cylindrical symmetry. Nonlinear Analysis., 55 (2003) 217232.
Z.Wang, H. Zhou; Solutions for a nonhomogeneous elliptic problem involving critical Sobolev-Hardy exponent in RN, Acta Math. Sci. 26 (2006) 525-536.
M. Willem; Minimax Theorems, Progress in Nonlinear Differential Equations and their Applications 24, Birkhauser Boston, Boston, MA, 1996.
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