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October 2021 Uniqueness of positive solutions for a class of p-Kirchhoff type problems with singularity
Yu Duan, Hong-Ying Li, Xin Sun
Rocky Mountain J. Math. 51(5): 1629-1637 (October 2021). DOI: 10.1216/rmj.2021.51.1629

Abstract

The singular Kirchhoff-type p-Laplacian problem

(a+bΩ|u|pdx)Δpu=f(x)uγλuq,xΩ,u>0,xΩ,u=0,xΩ,

is considered, where ΩN(N3) is a bounded domain, a,b0 with

a+b>0,λ0,0<γ<1<p<N,0<qp1,

p=pN(Np) is the critical Sobolev exponent, and the coefficient f is in Lp(p+γ1)(Ω) with f(x)>0. By the variational method and some analysis techniques, a uniqueness result for a class of singular p-Kirchhoff type problems is obtained.

Citation

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Yu Duan. Hong-Ying Li. Xin Sun. "Uniqueness of positive solutions for a class of p-Kirchhoff type problems with singularity." Rocky Mountain J. Math. 51 (5) 1629 - 1637, October 2021. https://doi.org/10.1216/rmj.2021.51.1629

Information

Received: 2 July 2018; Revised: 2 October 2018; Accepted: 16 November 2018; Published: October 2021
First available in Project Euclid: 17 February 2022

Digital Object Identifier: 10.1216/rmj.2021.51.1629

Subjects:
Primary: 35A15 , 35J62 , 35J75

Keywords: p-Kirchhoff type problem , singularity , uniqueness , variational method

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.51 • No. 5 • October 2021
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