Electron. J. Differential Equations, Vol. 2025 (2025), No. 88, pp. 1-23.

Multiple solutions for parametric weighted (p,q)-equations

Xiaohui Zhang, Xian Xu

Abstract:
In this article, we prove that equations driven by a weighted (p,q)-Laplacian have at least two positive solutions, two negative solutions, and two sign-changing solutions. To obtain these result, we construct an operator that has invariant sets consisting of supersolustions and subsolutions. Then using this operator, we find a locally Lipschitz continuous operator and use it to construct a descending flow. Finally, by the method of invariant sets of descending flow, we obtain the 6 solutions stated above.

Submitted May 7, 2025. Published September 11, 2025
Math Subject Classifications: 35D30, 35J60, 35J92, 47K10, 58R05.
Key Words: Invariant sets with descending flow; multiple solutions; parametric weighted (p,q)-equations.
DOI: 10.58997/ejde.2025.88

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Xiaohui Zhang
Department of Mathematics
Jiangsu Normal University
Xuzhou, Jiangsu 221116, China
email: 2607347563@qq.com
Xian Xu
Department of Mathematics
Jiangsu Normal University
Xuzhou, Jiangsu 221116, China
email: xuxian68@163.com

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