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

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

Electron. J. Differ. Equ. 1996(7), (1996)


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.

Mathematics Subject Classification

35A05, 35A15, 35J20


radial solutions, critical Sobolev exponents, palais-Smale condition, mountain pass theorem