For the equation −Δu=||xα|−2|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.
Multiple solutions for a Hénon-like equation on the annulus / M. Calanchi, S. Secchi, E. Terraneo. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 245:6(2008 Sep 15), pp. 1507-1525.
Multiple solutions for a Hénon-like equation on the annulus
M. CalanchiPrimo
;E. TerraneoUltimo
2008
Abstract
For the equation −Δu=||xα|−2|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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