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Anisotropic singular double phase Dirichlet problems

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  • We consider an anisotropic double phase problem with a reaction in which we have the competing effects of a parametric singular term and a superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter varies on $ \mathring{\mathbb{R}}_+ = (0, +\infty) $. Our approach uses variational tools together with truncation and comparison techniques as well as several general results of independent interest about anisotropic equations, which are proved in the Appendix.

    Mathematics Subject Classification: Primary: 35J75; Secondary: 35A16, 35B50, 35B51, 35J20, 35J60, 47J15, 58E05, 58E07.

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