Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 88, pp. 1-23.

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

Authors: Xiaohui Zhang (Jiangsu Normal Univ., Xuzhou, Jiangsu, China)
         Xian Xu (Jiangsu Normal Univ., Xuzhou, Jiangsu, China)

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.