Existence results for singular double phase problems by topological degree

In this paper we consider singular elliptic problems directed by the double phase operator, including a gradient-dependent reaction term as well as Dirichlet boundary conditions. Using topological degree methods for a class of non-continuous operators based on the abstract Hammerstein equation, we prove the existence of weak solutions in the Musielak-Orlicz-Sobolev space W₀1,E(O). Our assumptions are appropriate and different from those discussed above.