Multiple Solutions for a Henon-Like Equation on the Annulus
Abstract
For the equation (- u = | |x|-2 |α up-1), (1 < |x| < 3), we prove the existence of two solutions for (α) large, and of two additional solutions when (p) is close to the critical Sobolev exponent (2*=2N/(N-2)). A symmetry--breaking phenomenon appears, showing that the least--energy solutions cannot be radial functions.
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