Geodesic
Radially symmetric solutions for a class of critical exponent elliptic problems in \(\mathbb R^ N\)
Electronic journal of differential equations, Tome 1996 (1996) no. 7
We give a method for obtaining radially symmetric solutions for the critical exponent problem

$\left\{ \eqalign{ -\Delta u+a(x)u=\ \lambda u^q+u^{2^*-1}{\rm\ in\ } R^N \cr u{\rm greater thn 0 and\ }\\int_{R^N}|\nabla u|^2 less than \infty\cr } \right. $

where, outside a ball centered at the origin, the non-negative function a is bounded from below by a positive constant $a_o$. We remark that, differently from the literature, we do not require any conditions on a at infinity.
Classification : 35A05, 35A15, 35J20
Keywords: radial solutions, critical Sobolev exponents, palais-Smale condition, mountain pass theorem 
@article{EJDE_1996__1996_7_a0,
     author = {Alves,  C.O. and de Morais Filho,  D.C. and Souto,  M.A.S.},
     title = {Radially symmetric solutions for a class of critical exponent elliptic problems in \(\mathbb {R^} {N\)}},
     journal = {Electronic journal of differential equations},
     year = {1996},
     volume = {1996},
     number = {7},
     zbl = {0853.35032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1996__1996_7_a0/}
}
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%J Electronic journal of differential equations
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%F EJDE_1996__1996_7_a0
Alves,  C.O.; de Morais Filho,  D.C.; Souto,  M.A.S. Radially symmetric solutions for a class of critical exponent elliptic problems in \(\mathbb R^ N\). Electronic journal of differential equations, Tome 1996 (1996) no. 7. http://geodesic.mathdoc.fr/item/EJDE_1996__1996_7_a0/