We prove the existence of a bounded positive solution of a semilinear elliptic equation involving a supercritical exponent. Using the Lusternik-Schnirelman theory of critical points we also obtain the existence of multiple solutions.
"Existence theorems for elliptic equations involving supercritical Sobolev exponent." Adv. Differential Equations 2 (2) 231 - 256, 1997.