Rocky Mountain Journal of Mathematics

Multiple solutions for a Kirchhoff-type problem involving nonlocal fractional $p$-Laplacian and concave-convex nonlinearities

Chang-Mu Chu, Jiao-Jiao Sun, and Zhi-Peng Cai

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Abstract

This paper examines a class of Kirchhoff nonlocal operators involving concave-convex nonlinearities and sign-changing weight functions. With the aid of the Nehari manifold, the existence of multiple nontrivial nonnegative solutions is obtained.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 6 (2017), 1803-1823.

Dates
First available in Project Euclid: 21 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1511254953

Digital Object Identifier
doi:10.1216/RMJ-2017-47-6-1803

Mathematical Reviews number (MathSciNet)
MR3725245

Zentralblatt MATH identifier
1379.35114

Subjects
Primary: 35A15: Variational methods 35J60: Nonlinear elliptic equations 35S15: Boundary value problems for pseudodifferential operators

Keywords
Kirchhoff-type problem fractional $p$-Laplacian concave-convex nonlinearities sign-changing weight functions Nehari manifold

Citation

Chu, Chang-Mu; Sun, Jiao-Jiao; Cai, Zhi-Peng. Multiple solutions for a Kirchhoff-type problem involving nonlocal fractional $p$-Laplacian and concave-convex nonlinearities. Rocky Mountain J. Math. 47 (2017), no. 6, 1803--1823. doi:10.1216/RMJ-2017-47-6-1803. https://projecteuclid.org/euclid.rmjm/1511254953


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