On a double phase problem of Kirchhoff-type with variable exponent

This work discusses a class of double phase variable exponent problems of Kirchhoff-type. By utilizing sub-supersolutions method in certain appropriate Musielak-Orlicz Sobolev space, we establish the existence of at least one nonnegative solution. Furthermore, with the help of additional assumption on the nonlinearity, a second nonnegative solution is obtained by employing variational arguments.