Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 14, Issue 3, Pages 329-344Publisher
SPRINGER-VERLAG
DOI: 10.1007/s005260100105
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Variational techniques are applied to prove the existence of standing wave solutions for quasilinear Schrodinger 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) = integral \delu\(2)u(2) are substantially different from the semilinear case.
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