On positive solutions for a class of double phase problems with strong singular weights and nonlinearities

We study the existence and nonexistence of positive solutions for the singular double phase problem:-where > 0, 1 < p < q < , and m (s) := |s| m-2 s.This model can contain strong singular weights and nonlinearities such as h(t) = t - with 1 and f (u) = 1 + u - with 1.Firstly, we provide sufficient conditions on , , and h such that positive solutions belong to C[0, 1], which generalizes previous results.Secondly, we establish various existence results, including the existence of three positive solutions, which are new results even for strong singular p-Laplacian problems.We prove the existence results by applying approximation techniques, resulting in approximation solutions that are not in C 1 [0, 1], stemming from the degeneracy of and .