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Uniqueness of the ground state solutions of quasilinear Schrödinger equations. (English) Zbl 1232.35067
Summary: We are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equations arising from plasma physics. We convert a quasilinear elliptic equation into a semilinear one and show the unique existence of a positive radial solution for the original equation under the suitable conditions on the power of nonlinearity and quasilinearity. We also investigate the non-degeneracy of a positive radial solution for a converted semilinear elliptic equation.
MSC:
35J62Quasilinear elliptic equations
35A02Uniqueness problems for PDE: global uniqueness, local uniqueness, non-uniqueness
82D10Plasmas (statistical mechanics)
35J61Semilinear elliptic equations
35Q41Time-dependent Schrödinger equations, Dirac equations
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