TY - JOUR
T1 - Infinitely Many Solutions for an Elliptic Problem with Critical Exponent in Exterior Domain
JO - Journal of Partial Differential Equations
VL - 1
SP - 80
EP - 104
PY - 2010
DA - 2010/02
SN - 23
DO - http://doi.org/10.4208/jpde.v23.n1.5
UR - https://global-sci.org/intro/article_detail/jpde/5223.html
KW - Infinitely many solutions
KW - critical exponent
KW - exterior domain
AB - <p>We consider the following nonlinear problem -Δu=u^{\frac{N+2}{N-2}}, u &gt; 0, in R^N\Ω, u(x)→ 0, as |x|→+∞, \frac{∂u}{∂n}=0, on ∂Ω, where Ω⊂R^N N ≥ 4 is a smooth and bounded domain and n denotes inward normal vector of ∂Ω. We prove that the above problem has infinitely many solutions whose energy can be made arbitrarily large when Ω is convex seen from inside (with some symmetries).</p>