School of Mathematics
Sichuan University
Chengdu 610064, China
email: shuwenxueyi@163.com
School of Mathematics
Sichuan University
Chengdu 610064, China
email: zhangshiqing@scu.edu.cn
Shuwen He, Shiqing Zhang
Abstract:
In this article we study the fractional \(p\)-Laplacian Kirchhoff type problem in
\(\mathbb{R}^N\),
$$
\Big(a+b\int\int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+sp}}\,dx\,dy\Big)
(-\Delta)_p^s u+\lambda V(x)|u|^{p-2}u=f(x,u)+g(x,u),
$$
where \(s\in(0,1), 2\leq p< \infty, N>sp\), \(a, b, \lambda >0\) are parameters.
Under suitable assumptions on \(V, f\) and \(g\), if \(b\) is sufficiently small and
\(\lambda\) is large enough, we show that the existence of at least two different
nontrivial solutions by combining the variational methods and the truncation
technique. At the same time, we explore the asymptotic behavior of solutions as
\(b\to 0\) and \(\lambda\to \infty\). We also obtain the nonexistence of nontrivial
solutions when \(a\) is large enough.
Submitted November 5, 2025. Published February 17, 2026.
Math Subject Classifications: 35A15, 35R11, 35B40.
Key Words: Fractional p-Laplacian; Kirchhoff type problems; variational methods;
truncation technique.
DOI: 10.58997/ejde.2026.15
Show me the PDF file (474 KB), TEX file for this article.
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Shuwen He School of Mathematics Sichuan University Chengdu 610064, China email: shuwenxueyi@163.com |
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Shiqing Zhang School of Mathematics Sichuan University Chengdu 610064, China email: zhangshiqing@scu.edu.cn |
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