Geodesic
Multiple positive solutions for equations involving critical Sobolev exponent in \(\mathbb{R}^ N\)
Electronic journal of differential equations, Tome 1997 (1997)
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__a31,
     author = {Alves,  C.O.},
     title = {Multiple positive solutions for equations involving critical {Sobolev} exponent in {\(\mathbb{R}^} {N\)}},
     journal = {Electronic journal of differential equations},
     year = {1997},
     volume = {1997},
     zbl = {0886.35056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a31/}
}
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TI  - Multiple positive solutions for equations involving critical Sobolev exponent in \(\mathbb{R}^ N\)
JO  - Electronic journal of differential equations
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VL  - 1997
UR  - http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a31/
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%A Alves,  C.O.
%T Multiple positive solutions for equations involving critical Sobolev exponent in \(\mathbb{R}^ N\)
%J Electronic journal of differential equations
%D 1997
%V 1997
%U http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a31/
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%F EJDE_1997__1997__a31
Alves,  C.O. Multiple positive solutions for equations involving critical Sobolev exponent in \(\mathbb{R}^ N\). Electronic journal of differential equations, Tome 1997 (1997). http://geodesic.mathdoc.fr/item/EJDE_1997__1997__a31/