Solutions for a quasilinear Schrödinger equation: a dual approach

We consider quasilinear stationary Schrödinger equations of the form (1) − Δu− Δ(u 2)u=g(x,u), x∈ R N. Introducing a change of unknown, we transform the search of solutions u( x) of (1) into the search of solutions v( x) of the semilinear equation (2) − Δv= 1 1+2f 2(v) g(x,f(v)), x∈ R N, where f is...

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Bibliographic Details
Published in:Nonlinear analysis 2004, Vol.56 (2), p.213-226
Main Authors: Colin, Mathieu, Jeanjean, Louis
Format: Article
Language:English
Subjects:
Analysis of PDEs
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Minimax methods
Partial differential equations
Quasilinear Schrödinger equations
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:We consider quasilinear stationary Schrödinger equations of the form (1) − Δu− Δ(u 2)u=g(x,u), x∈ R N. Introducing a change of unknown, we transform the search of solutions u( x) of (1) into the search of solutions v( x) of the semilinear equation (2) − Δv= 1 1+2f 2(v) g(x,f(v)), x∈ R N, where f is suitably chosen. If v is a classical solution of (2) then u= f( v) is a classical solution of (1). Variational methods are then used to obtain various existence results.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2003.09.008