In this chapter we are interested in equations given in potential form, i.e. equations that arise from equating to zero the Gâteaux derivative of certain Euler action functionals. When the action functional is continuous and coercive but lacks sequential weak lower semicontinuity, we cannot apply the Weierstrass–Tonelli theorem, but we can still obtain the existence of finite-dimensional approximations and investigate their convergence. Thereby, we obtain a new notion of variational generalized solution, which is introduced in this chapter in an abstract form and then illustrated by the solvability of problems involving the competing (p, q)-Laplacian with unbounded weight in the leading term.