Radially symmetric solutions for a class of critical exponent elliptic problems in $\Bbb R\sp N$

Alves, C.O.; de Morais Filho, D.C.; Souto, M.A.S.

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Radially symmetric solutions for a class of critical exponent elliptic problems in $\Bbb R\sp N$

Alves, C.O. ; de Morais Filho, D.C. ; Souto, M.A.S.

Electronic Journal of Differential Equations, Tome 1996 (1996) no. 7.

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

Résumé

Summary: 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

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     title = {Radially symmetric solutions for a class of critical exponent elliptic problems in $\Bbb R\sp N$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1996},
     number = {7},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1996__1996_7_a0/}
}

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Alves, C.O.; de Morais Filho, D.C.; Souto, M.A.S. Radially symmetric solutions for a class of critical exponent elliptic problems in $\Bbb R\sp N$. Electronic Journal of Differential Equations, Tome 1996 (1996) no. 7. http://geodesic.mathdoc.fr/item/EJDE_1996__1996_7_a0/