This analysis reveals six solutions for weighted (p,q)-Laplacian equations, indicating the effectiveness of the method using invariant sets and descending flow.
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. For more information see https://ejde.math.txstate.edu/Volumes/2025/88/abstr.html
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Zhang et al. (2025) studied this question.
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