Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
Volume 14, Issue 12, Pages 4465-4502Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdss.2021111
Keywords
Anisotropic p-Laplacian; singular term; bounded solution; Moser iteration; truncation; maximum principle; comparison principle; bifurcation-type result
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Funding
- Fundamental Research Funds for the Central Universities of Central South University [2019zzts211]
- China Scholarship Council [201906370079]
- Slovenian Research Agency program [P1-0292]
- Romanian Ministry of Research, Innovation and Digitization, CNCS/CCCDI-UEFISCDI, within PNCDI III [PCE 137/2021]
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This study examines an anisotropic double phase problem with a reaction, involving the competing effects of a parametric singular term and a superlinear perturbation. By utilizing variational tools, truncation and comparison techniques, as well as general results on anisotropic equations, the changes in the set of positive solutions as the parameter varies on R+ = (0, +infinity) are described through a bifurcation-type result.
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 R+ = (0, +infinity). 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.
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