INFINITELY MANY SOLUTIONS FOR A <i>P</i>-SUPERLINEAR <i>P</i>-LAPLACIAN PROBLEMS

Lijuan Yang; Ruyun Ma

doi:10.11948/20230394

2024 Volume 14 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(3): 1778-1789

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Lijuan Yang, Ruyun Ma. INFINITELY MANY SOLUTIONS FOR A P-SUPERLINEAR P-LAPLACIAN PROBLEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1778-1789. doi: 10.11948/20230394

Citation:

Lijuan Yang, Ruyun Ma. INFINITELY MANY SOLUTIONS FOR A P-SUPERLINEAR P-LAPLACIAN PROBLEMS[J]. Journal of Applied Analysis & Computation, 2024, 14(3): 1778-1789. doi: 10.11948/20230394

INFINITELY MANY SOLUTIONS FOR A P-SUPERLINEAR P-LAPLACIAN PROBLEMS

Lijuan Yang^1,,
Ruyun Ma^1,2, ,

1.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2.
School of Mathematics and Statistics, Xidian University, Xi'an 710071, China

Author Bio: Email: yanglj97@163.com(L. Yang)
Corresponding author: Email: mary@nwnu.edu.cn(R. Ma)
Fund Project: The authors were supported by National Natural Science Foundation of China (12061064) and Shaanxi Fundamental Science Research Project for Mathematics and Physics (22JSY018)

Abstract

Abstract

We are concerned with the existence of infinitely many solutions for $ p $-Laplacian problem
$ \left\{\begin{array}{l}-\left(\varphi_p\left(u^{\prime}\right)\right)^{\prime}=g(u)+h\left(x, u, u^{\prime}\right), \quad x \in(0,1), \\u(0)=u(1)=0,\end{array}\right.\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(P) $
where $ \varphi_p(s):=|s|^{p-2}\cdot s $, $ p>1 $, $ g:\mathbb{R}\to\mathbb{R} $ is a continuous function and satisfies $ p $-superlinear growth at infinity, $ h:[0, 1]\times\mathbb{R}^2\to\mathbb{R} $ is a continuous function satisfying $ |h(x, \xi, \xi_1)|\leqslant C+\frac{1}{2}|\varphi_p(\xi)| $. Based on global bifurcation techniques, we obtain infinitely many solutions of $ (P) $ having specified nodal properties.
- Solutions /
- p-Laplacian /
- p-superlinear /
- bifurcation
MSC: 34B05, 35B32

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References

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