In this paper we consider the following class of fractional Kirchhoff equations with critical growth: (equations presented) where ϵ > 0 is a small parameter, a, b > 0 are constants, s ϵ (3/4, 1), 2∗s = 6/3-2s is the fractional critical exponent, (-δ)s is the fractional Laplacian operator, V is a positive continuous potential and f is a superlinear continuous function with subcritical growth. Using penalization techniques and variational methods, we prove the existence of a family of positive solutions uϵ which concentrates around a local minimum of V as ϵ → 0.

Concentrating solutions for a fractional Kirchhoff equation with critical growth / Ambrosio, V.. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 116:3-4(2020), pp. 249-278. [10.3233/ASY-191543]

Concentrating solutions for a fractional Kirchhoff equation with critical growth

Ambrosio V.
2020-01-01

Abstract

In this paper we consider the following class of fractional Kirchhoff equations with critical growth: (equations presented) where ϵ > 0 is a small parameter, a, b > 0 are constants, s ϵ (3/4, 1), 2∗s = 6/3-2s is the fractional critical exponent, (-δ)s is the fractional Laplacian operator, V is a positive continuous potential and f is a superlinear continuous function with subcritical growth. Using penalization techniques and variational methods, we prove the existence of a family of positive solutions uϵ which concentrates around a local minimum of V as ϵ → 0.
2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/278518
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