Existence and multiplicity of solutions for a new <i>p</i>(<i>x</i>)-Kirchhoff equation-Reference-Cited by-同舟云学术

Existence and multiplicity of solutions for a new p(x)-Kirchhoff equation

Published:2024-01-01 Issue:1 Volume:13 Page:
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Chu Changmu¹,Liu Jiaquan²

Affiliation:

1. School of Preparatory Education, Guizhou Minzu University , Guizhou 550025 , P.R. China

2. LMAM, School of Mathematical Science, Peking University , Beijing 100871 , P.R. China

Abstract

Abstract This article is devoted to study a class of new

p ( x )

p\left(x)

-Kirchhoff equation. By means of perturbation technique, variational method, and the method invariant sets for the descending flow, the existence and multiplicity of solutions to this problem are obtained.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/anona-2024-0018/pdf

Reference33 articles.

1. A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 4 (1973), 349–381.

2. S. N. Antontsev and S. I. Shmarev, A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions, Nonlinear Anal. 60 (2005), no. 3, 515–545.

3. W. C. Bu, T. Q. An, G. J. Ye, and S. Taarabti, Negative energy solutions for a new fractional p(x)-Kirchhoff problem without the (AR) condition, J. Funct. Spaces 2021 (2021), Art ID 8888078, 13pp.

4. Y. M. Chen, S. Levine, and M. Rao, Variable exponent, linear growth functionals in image processing, Siam J. Appl. Math. 66 (2006), 1383–1406.

5. C. M. Chu, Positive solutions for a class of p(x)-Laplacian equation involving concave-convex nonlinearities, Adv. Differential Equations 26 (2021), 341–362.