Existence of solutions for a class of fractional Kirchhoff variational inequality

Shenbing Deng; Wenshan Luo; César E. Torres Ledesma; George W. Alama Quiroz

doi:10.4171/zaa/1742

JournalszaaVol. 43, No. 1/2pp. 149–168

Existence of solutions for a class of fractional Kirchhoff variational inequality

Shenbing Deng
Southwest University, Chongqing, China
Wenshan Luo
Southwest University, Chongqing, China
César E. Torres Ledesma
Universidad Nacional de Trujillo, Peru
George W. Alama Quiroz
Universidad Privada del Norte, Trujillo, Peru

$Existence of solutions for a class of fractional Kirchhoff variational inequality cover$

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Abstract

We are concerned with the following fractional Kirchhoff variational inequality:

(a + b [u]^{2}) \int_{R^{3}} (- Δ)^{\frac{s}{2}} u (- Δ)^{\frac{s}{2}} (v - u) d x + \int_{R^{3}} (1 + λV (x)) u (v - u) d x \geq \int_{R^{3}} f (u) (v - u) d x \forall v \in K,

where $s \in (\frac{3}{4}, 1)$ , $λ > 0$ . In this paper, by applying penalization techniques from Bensoussan and Lions (1978) combined with mountain pass theorem, we show the existence and concentration behavior of positive solution to the cited variational inequality. This result extend some results established by Alves, Barros and Torres [J. Math. Anal. Appl. 494 (2021)] to the fractional case.

Cite this article

Shenbing Deng, Wenshan Luo, César E. Torres Ledesma, George W. Alama Quiroz, Existence of solutions for a class of fractional Kirchhoff variational inequality. Z. Anal. Anwend. 43 (2024), no. 1/2, pp. 149–168

DOI 10.4171/ZAA/1742