Dynamics of Partial Differential Equations

Volume 17 (2020)

Number 2

Least energy sign-changing solution to a fractional $p$-Laplacian problem involving singularities

Pages: 97 – 115

DOI: https://dx.doi.org/10.4310/DPDE.2020.v17.n2.a1

Authors

S. Ghosh (Department of Mathematics, National Institute of Technology Rourkela, India)

K. Saoudi (College of Sciences at Dammam, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia; and Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia)

M. Kratou (College of Sciences at Dammam, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia; and Basic and Applied Scientific Research Center, Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia)

D. Choudhuri (Department of Mathematics, National Institute of Technology Rourkela, India)

Abstract

In this paper we study the existence of a least energy sign-changing solution to a nonlocal elliptic PDE involving singularities by using the Nehari manifold method, the constraint variational method and Brouwer degree theory.

Keywords

sign-changing solutions, fractional $p$-Laplacian, Nehari manifold, singularity, Brouwer degree

2010 Mathematics Subject Classification

47J30, 35J60, 35J92, 35R11

Full Text (PDF format)

S. Ghosh thanks the Council of Scientific and Industrial Research (CSIR), India, for the financial support vide grant no. 09/983(0013)/2017-EMR-I.

D. Choudhuri thanks the Council of Scientific and Industrial Research (CSIR), India, for research grant vide grant no. 25(0292)/18 /EMR-II.

Received 21 October 2019

Published 24 February 2020