Geodesic
Multiple positive solutions for equations involving critical Sobolev exponent in $\bbfR\sp N$
Electronic Journal of Differential Equations, Tome 1997 (1997).

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

Summary: This article concerns with the problem $$ -{\rm div }(|\nabla u|^{m-2}\nabla u) = \lambda h u^q+u^{m^*-1},\quad{\rm in}\quad {\Bbb R}^N\,. $$ Using the Ekeland Variational Principle and the Mountain Pass Theorem, we show the existence of $\lambda ^*>0$ such that there are at least two non-negative solutions for each $\lambda$ in $(0,\lambda ^*)$.
Classification : 35J20, 35J25
Keywords: mountain pass theorem, Ekeland variational principle 
@article{EJDE_1997__1997__a7,
     author = {Alves, C.O.},
     title = {Multiple positive solutions for equations involving critical {Sobolev} exponent in $\bbfR\sp N$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1997},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a7/}
}
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Alves, C.O. Multiple positive solutions for equations involving critical Sobolev exponent in $\bbfR\sp N$. Electronic Journal of Differential Equations, Tome 1997 (1997). http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a7/