Abstract
We use the mountain-pass theorem combined with the principle of symmetric criticality to establish multiplicity of solutions for the class of quasilinear elliptic equations
-Δu + V(z)u - Δ(u2)u = h(u) in ℝN
where N ≥ 4, the potential V : ℝN → ℝ is positive and bounded away from zero and satisfies appropriate periodic and symmetric conditions. The nonlinear term h(u) has subcritical growth and satisfies a condition of the Ambrosetti-Rabinowitz type. Schrödinger equations of this type have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics.
Keywords: Quasilinear Schr¨odinger equation; standing wave solutions; mountain-pass theorem; principle of symmetric criticality
Received: 2007-10-08
Published Online: 2016-03-10
Published in Print: 2008-05-01
© 2016 by Advanced Nonlinear Studies, Inc.
