Geodesic
Nonhomogeneous elliptic equations involving critical Sobolev exponent and weight
Electronic Journal of Differential Equations, Tome 2016 (2016).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article we consider the problem $$\displaylines{ -\hbox{div}\big(p(x)\nabla u\big)=|u|^{2^{*}-2}u+\lambda f\quad {in }\Omega \cr u=0 \quad {on }\partial\Omega }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$, We study the relationship between the behavior of p near its minima on the existence of solutions.
Classification : 35J20, 35J25, 35J60
Keywords: critical Sobolev exponent, Nehari manifold, variational principle 
@article{EJDE_2016__2016__a51,
     author = {Bouchekif, Mohammed and Rimouche, Ali},
     title = {Nonhomogeneous elliptic equations involving critical {Sobolev} exponent and weight},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2016},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a51/}
}
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Bouchekif, Mohammed; Rimouche, Ali. Nonhomogeneous elliptic equations involving critical Sobolev exponent and weight. Electronic Journal of Differential Equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a51/