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.

Bifurcation results for a fractional elliptic equation with critical exponent in Rn / S. Dipierro, M. Medina, I. Peral, E. Valdinoci. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 153:1-2(2017 May), pp. 183-230. [10.1007/s00229-016-0878-3]

Bifurcation results for a fractional elliptic equation with critical exponent in Rn

S. Dipierro
Primo
;
E. Valdinoci
Ultimo
2017-05

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.
35B40; 35D30; 35J20; 35R11; 49N60; mathematics (all)
Settore MAT/05 - Analisi Matematica
12-ago-2016
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/505149
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