Existence of solutions for a singular double phase in Sobolev-Orlicz spaces with variable exponents in a complete manifold

The purpose of this paper is to study a class of double phase problems, with a singular term and a superlinear parametric term on the right-hand side. Using the method of Nehari manifold combined with the fibering maps, we prove that for all small values of the parameter λ > 0, there exist at least two non-trivial positive solutions. Our results extend the previous works Papageorgiou, Repovus, and Vetro [24] and Liu, Dai, Papageorgiou, and Winkert [21], from the case of Musielak-Orlicz Sobolev space, when exponents p and q are constant, to the case of Sobolev-Orlicz spaces with variable exponents in a complete manifold.

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