December 2023 EXISTENCE OF GROUND STATES TO THE DOUBLE-TYPE NONLINEAR p-LAPLACE PROBLEM INVOLVING SOBOLEV CRITICAL EXPONENT
Yunfeng Cui, Shiwang Ma, Lixia Wang
Rocky Mountain J. Math. 53(6): 1749-1765 (December 2023). DOI: 10.1216/rmj.2023.53.1749

Abstract

We extend the results of Akahori et al. (2019) on ground states. We discuss the existence of ground states to the double-type nonlinear p-Laplace problem involving the Sobolev critical exponent in RN:

Δpu+|u|p2u=|u|p2u+λ|u|q2u,uW1,p(RN),

where N2, λ>0, 1<p<N, p<q<p, pNp(Np) is the Sobolev critical index, Δpu=div(|u|p2u) is the p-Laplace operator. We show that: (i) if p<q<p, then there exists λ0>0 so that ground states exist for all λ>λ0; (ii) if max (p,ppp1)<q<p, then there exist ground states for all λ>0.

Citation

Download Citation

Yunfeng Cui. Shiwang Ma. Lixia Wang. "EXISTENCE OF GROUND STATES TO THE DOUBLE-TYPE NONLINEAR p-LAPLACE PROBLEM INVOLVING SOBOLEV CRITICAL EXPONENT." Rocky Mountain J. Math. 53 (6) 1749 - 1765, December 2023. https://doi.org/10.1216/rmj.2023.53.1749

Information

Received: 22 April 2022; Revised: 30 October 2022; Accepted: 31 October 2022; Published: December 2023
First available in Project Euclid: 21 December 2023

MathSciNet: MR4682740
zbMATH: 07784572
Digital Object Identifier: 10.1216/rmj.2023.53.1749

Subjects:
Primary: 35J20
Secondary: 35J60

Keywords: Embedding theorem , Mountain Pass Lemma , Nehari manifold , p-Laplace , Sobolev critical index

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 6 • December 2023
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