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Advanced Nonlinear Studies

Editor-in-Chief: Ahmad, Shair

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Volume 8, Issue 2


Symmetric And Nonsymmetric Solutions For a Class of Quasilinear Schrödinger Equations

Uberlandio B. Severo
Published Online: 2016-03-10 | DOI: https://doi.org/10.1515/ans-2008-0208


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

About the article

Received: 2007-10-08

Published Online: 2016-03-10

Published in Print: 2008-05-01

Citation Information: Advanced Nonlinear Studies, Volume 8, Issue 2, Pages 375–389, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2008-0208.

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