In this manuscript, existence and multiplicity results are obtained for a problem involving an anisotropic $(p,q)$-Laplacian-type operator by means of sub-supersolutions and variational techniques. This problem arises in various applications such as in the study of the enhancement of images, the spread of epidemic disease and in the dynamic of fluids. Under a general condition, the existence of a solution is proved, and the multiplicity of solutions is obtained by considering an additional natural hypothesis.