Geodesic
Multiple solvability of certain elliptic problems with critical nonlinearity exponents
Matematičeskie zametki, Tome 52 (1992) no. 1, pp. 51-56 
I. A. Kuzin. Multiple solvability of certain elliptic problems with critical nonlinearity exponents. Matematičeskie zametki, Tome 52 (1992) no. 1, pp. 51-56. http://geodesic.mathdoc.fr/item/MZM_1992_52_1_a7/
@article{MZM_1992_52_1_a7,
     author = {I. A. Kuzin},
     title = {Multiple solvability of certain elliptic problems with critical nonlinearity exponents},
     journal = {Matemati\v{c}eskie zametki},
     pages = {51--56},
     year = {1992},
     volume = {52},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1992_52_1_a7/}
}
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%J Matematičeskie zametki
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that the problem $$ \sum_{i=1}^N\nabla_i(|\nabla u|^{p-2}\nabla_iu)+|u|^{p^*-2}u+\lambda|u|^{q-2}u=0 \text{ in } \Omega, \quad u=0 \text{ on } \partial\Omega, $$ where $\Omega\subset\mathbf{R}^N$ a singly-connected region with an “odd” boundary, $N>p$, and $p^*=Np/(N-p)$ is a critical Sobolev exponent, has, under the appropriate conditions on $\lambda$, $q$ and $N$, no less than $(2N+2)$ nontrivial solutions in $\mathring{W}_{p^1}(\Omega)$.