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Infinitely Many Solutions for Kirchhoff-Type Equations Involving Degenerate Operator

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Abstract

In this paper, we study the existence of infinitely many nontrivial solutions for a class of nonlinear Kirchhoff-type equation

$$-\left(a+b\int\limits_{\mathbb{R}^{N}}|\nabla_{\lambda}u|^{2}dx\right)\Delta_{\lambda}u+V(x)u=f(x,u),\quad\text{in }\mathbb{R}^{N}$$

where constants \(a>0,\ b>0\), \(\Delta_{\lambda}\) is a strongly degenerate elliptic operator, and \(f\) is a function with a more general superlinear conditions or sublinear conditions.

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Funding

This work is supported by Research Fund of National Natural Science Foundation of China (no. 11861046), Chongqing Municipal Education Commission (no. KJQN20190081), Chongqing Technology and Business University(no. CTBUZDPTTD201909), Graduate Innovation Project of Chongqing Technology and Business University (yjscxx2021-112-109).

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Authors and Affiliations

  1. Chongqing Technology and Business University, Chongqing, China

    J. Chen, L. Li & Sh. Chen

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  1. J. Chen
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  2. L. Li
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  3. Sh. Chen
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Correspondence to J. Chen, L. Li or Sh. Chen.

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Chen, J., Li, L. & Chen, S. Infinitely Many Solutions for Kirchhoff-Type Equations Involving Degenerate Operator. J. Contemp. Mathemat. Anal. 57, 252–266 (2022). https://doi.org/10.3103/S1068362322040045

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