Abstract
In this paper we study some nonlinear elliptic equations in Rn obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is (-Δ)su=εhu+q+u+pinRn,where s∈ (0 , 1) , n> 4 s, ε> 0 is a small parameter, p=n+2sn-2s, 0 < q< p and h is a continuous and compactly supported function. To construct solutions to this equation, we use the Lyapunov–Schmidt reduction, that takes advantage of the variational structure of the problem. For this, the case 0 < q< 1 is particularly difficult, due to the lack of regularity of the associated energy functional, and we need to introduce a new functional setting and develop an appropriate fractional elliptic regularity theory.
| Original language | English |
|---|---|
| Pages (from-to) | 183-230 |
| Number of pages | 48 |
| Journal | Manuscripta Mathematica |
| Volume | 153 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 1 May 2017 |
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Bifurcation results for a fractional elliptic equation with critical exponent in Rn. / Dipierro, Serena; Medina, María; Peral, Ireneo; Valdinoci, Enrico.
In: Manuscripta Mathematica, Vol. 153, No. 1-2, 01.05.2017, p. 183-230.Research output: Contribution to journal › Article
TY - JOUR
T1 - Bifurcation results for a fractional elliptic equation with critical exponent in Rn
AU - Dipierro, Serena
AU - Medina, María
AU - Peral, Ireneo
AU - Valdinoci, Enrico
PY - 2017/5/1
Y1 - 2017/5/1
N2 - In this paper we study some nonlinear elliptic equations in Rn obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is (-Δ)su=εhu+q+u+pinRn,where s∈ (0 , 1) , n> 4 s, ε> 0 is a small parameter, p=n+2sn-2s, 0 < q< p and h is a continuous and compactly supported function. To construct solutions to this equation, we use the Lyapunov–Schmidt reduction, that takes advantage of the variational structure of the problem. For this, the case 0 < q< 1 is particularly difficult, due to the lack of regularity of the associated energy functional, and we need to introduce a new functional setting and develop an appropriate fractional elliptic regularity theory.
AB - In this paper we study some nonlinear elliptic equations in Rn obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is (-Δ)su=εhu+q+u+pinRn,where s∈ (0 , 1) , n> 4 s, ε> 0 is a small parameter, p=n+2sn-2s, 0 < q< p and h is a continuous and compactly supported function. To construct solutions to this equation, we use the Lyapunov–Schmidt reduction, that takes advantage of the variational structure of the problem. For this, the case 0 < q< 1 is particularly difficult, due to the lack of regularity of the associated energy functional, and we need to introduce a new functional setting and develop an appropriate fractional elliptic regularity theory.
KW - 35B40
KW - 35D30
KW - 35J20
KW - 35R11
KW - 49N60
UR - http://www.scopus.com/inward/record.url?scp=84982151943&partnerID=8YFLogxK
U2 - 10.1007/s00229-016-0878-3
DO - 10.1007/s00229-016-0878-3
M3 - Article
VL - 153
SP - 183
EP - 230
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
SN - 0025-2611
IS - 1-2
ER -