Abstract.
Variational techniques are applied to prove the existence of standing wave solutions for quasilinear Schrödinger equations containing strongly singular nonlinearities which include derivatives of the second order. Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Direct methods of the calculus of variations and minimax methods like the Mountain Pass Theorem are used. The difficulties introduced by the nonconvex functional \(\Phi(u)=\int |\nabla u|^2 u^2\) are substantially different from the semilinear case.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 21 March 2000 / Accepted: 23 February 2001 / Published online: 25 June 2001
Rights and permissions
About this article
Cite this article
Poppenberg, M., Schmitt, K. & Wang, ZQ. On the existence of soliton solutions to quasilinear Schrödinger equations. Calc Var 14, 329–344 (2002). https://doi.org/10.1007/s005260100105
Issue Date:
DOI: https://doi.org/10.1007/s005260100105