The Nehari manifold method for discrete fractional p-Laplacian equations-Reference-Cited by-同舟云学术

The Nehari manifold method for discrete fractional p-Laplacian equations

Published:2020-10-07 Issue:1 Volume:2020 Page:
ISSN:1687-1847
Container-title:Advances in Difference Equations
language:en
Short-container-title:Adv Differ Equ

Author:

Ju Xuewei,Die Hu,Xiang Mingqi

Abstract

AbstractThe aim of this paper is to investigate the multiplicity of homoclinic solutions for a discrete fractional difference equation. First, we give a variational framework to a discrete fractional p-Laplacian equation. Then two nontrivial and nonnegative homoclinic solutions are obtained by using the Nehari manifold method.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Link

https://link.springer.com/content/pdf/10.1186/s13662-020-03014-z.pdf

Reference37 articles.

1. Acosta, G., Borthagaray, J.P.: A fractional Laplace equation: regularity of solutions and finite element approximations. SIAM J. Numer. Anal. 55, 472–495 (2017)

2. Agarwal, R.P., Perera, K., O’Regan, D.: Multiple positive solutions of singular and nonsingular discrete problems via variational methods. Nonlinear Anal. 58, 69–73 (2004)

3. Ambrosio, L., De Philippis, G., Martinazzi, L.: Gamma-convergence of nonlocal perimeter functionals. Manuscr. Math. 134, 377–403 (2011)

4. Applebaum, D.: Lévy processes–from probability to finance quantum groups. Not. Am. Math. Soc. 51, 1336–1347 (2004)

5. Autuori, G., Pucci, P.: Elliptic problems involving the fractional Laplacian in $\mathbb{R}^{N}$. J. Differ. Equ. 255, 2340–2362 (2013)

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