In this chapter, we continue our investigation of variational problems. However, unlike previously, we do not impose the differentiability assumption on the Euler action functional. Instead, we assume that the functional is locally Lipschitz continuous. As a result, we do not deal with a standard equation but rather with a nonlinear inclusion. For such an inclusion, we introduce a concept of generalized solution and obtain the relevant existence result. We provide applications to problems driven by the perturbed (p, q)-competing Laplacian, which we introduce here, and also to competing problems in variable Sobolev spaces.