Abstract
We study a Dirichlet (p, q)-Laplacian elliptic problem. The reaction term possesses a parametric singular term \(\lambda u^{-\eta }\) (\(\lambda >0\) is the parameter and \(0<\eta <1\)) and of a Caratheodory perturbation f(z, u). We consider two different cases. In Case I, \(f(z,\cdot )\) is assumed to be \((p-1)\)-sublinear as \(x\rightarrow +\infty \), and in Case II, we assume that \(f(z,\cdot )\) is \((p-1)\)-superlinear but dispensing with the Ambrosetti–Rabinowitz condition. For both cases, we prove a multiplicity theorem which is global with respect to the parameter \(\lambda >0\).
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This work was supported by the National Natural Science Foundation of China (No. 12071098) and the Fundamental Research Funds for the Central Universities (No. 2022FRFK060022).
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Papageorgiou, N.S., Zhang, C. Global Multiplicity for the Positive Solutions of Parametric Singular (p, q)-equations with Indefinite Perturbations. Bull. Malays. Math. Sci. Soc. 46, 5 (2023). https://doi.org/10.1007/s40840-022-01427-5
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DOI: https://doi.org/10.1007/s40840-022-01427-5