Existence and nonexistence of positive solutions to a class of nonlocal discrete Kirchhoff type equations-Reference-Cited by-同舟云学术

Existence and nonexistence of positive solutions to a class of nonlocal discrete Kirchhoff type equations

Published:2023 Issue:10 Volume:8 Page:24568-24589
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Long Yuhua¹²

Affiliation:

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

2. Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China

Abstract

<abstract><p>In this paper, we investigate the existence and nonexistence of positive solutions to a class of nonlocal partial difference equations via a variant version of the mountain pass theorem. The conditions in our obtained results release the classical (AR) condition in some sense.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference27 articles.

1. C. O. Alves, F. J. S. A. Correa, T. F. Ma, Positive solutions for a quasilinear elliptic equation of Kirchhoff type, Comput. Math. Appl., 49 (2005), 85–93. https://doi.org/10.1016/j.camwa.2005.01.008

2. K. Perera, Z. T. Zhang, Nontrivial solutions of Kirchhoff-type problems via the Yang index, J. Differ. Equ., 221 (2006), 246–255. https://doi.org/10.1016/j.jde.2005.03.006

3. Z. T. Zhang, K. Perera, Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow, J. Math. Anal. Appl., 317 (2006), 456–463. https://doi.org/10.1016/j.jmaa.2005.06.102

4. A. M. Mao, Z. T. Zhang, Sign-changing and multiple solutions of Kirchhoff type problems without P.S. condition, Nonlinear Anal., 70 (2009), 1275–1287. https://doi.org/10.1016/j.na.2008.02.011

5. S. Gupta, G. Dwivedi, Ground state solution to N-Kirchhoff equation with critical exponential growth and without Ambrosetti-Rabinowitz condition, Rend. Circ. Mat. Palermo Ser. 2, 2023. https://doi.org/10.1007/s12215-023-00902-7

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