[COLLOQUIUM] Variational perturbations for a class of quasilinear elliptic equations

For a class of quasilinear elliptic problems including the modified nonlinear Schrodinger type equations, which lack both smoothness and compactness in the variational formulations, we discuss variational perturbation approaches for an existence theory. We review some early developments as  motivations for the new approaches. While our previous framework works effectively for constructing unbounded sequence of solutions, we also report some recent work on a different perturbation scheme which is more effective for another class of nonlinearity.