Multiple Solutions for Double Phase Problems with Hardy Type Potential

Chun-Bo Lian, Bei-Lei Zhang and Bin Ge
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Chun-Bo Lian: College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
Bei-Lei Zhang: College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
Bin Ge: College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China

Mathematics, 2021, vol. 9, issue 4, 1-19

Abstract: In this paper, we are concerned with the singular elliptic problems driven by the double phase operator and and Dirichlet boundary conditions. In view of the variational approach, we establish the existence of at least one nontrivial solution and two distinct nontrivial solutions under some general assumptions on the nonlinearity f . Here we use Ricceri’s variational principle and Bonanno’s three critical points theorem in order to overcome the lack of compactness.

Keywords: double phase operator; singular problem; variational methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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