In this paper we show the existence of non-negative solutions for a Kirchhoff type problem driven by a nonlocal integrodifferential operator, that is -M(∥-u∥-Z2) LKu=λf(x,u)+| u|2*-2u in Ω,u=0in Rn\-Ω where L K is an integrodifferential operator with kernel K, Ω is a bounded subset of Rn, M and f are continuous functions, ∥̇ ∥Z is a functional norm and 2* is a fractional Sobolev exponent.
A critical Kirchhoff type problem involving a nonlocal operator / A. Fiscella, E. Valdinoci. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 94:(2014), pp. 156-170. [10.1016/j.na.2013.08.011]
A critical Kirchhoff type problem involving a nonlocal operator
A. Fiscella;E. Valdinoci
2014
Abstract
In this paper we show the existence of non-negative solutions for a Kirchhoff type problem driven by a nonlocal integrodifferential operator, that is -M(∥-u∥-Z2) LKu=λf(x,u)+| u|2*-2u in Ω,u=0in Rn\-Ω where L K is an integrodifferential operator with kernel K, Ω is a bounded subset of Rn, M and f are continuous functions, ∥̇ ∥Z is a functional norm and 2* is a fractional Sobolev exponent.
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