Existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in ${\BR}^N$}

Details Existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in ${\BR}^N$} Existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in ${\BR}^N$}

2006-09-08

arxiv.org/abs/math/0609246v1

Mathematics

Analysis of PDEs

Scientific paper

Mountain pass in a suitable Orlicz space is employed to prove the existence of soliton solutions for a quasilinear Schr\"{o}dinger equation involving critical exponent in ${\BR}^N$. These equations contain strongly singular nonlinearities which include derivatives of the second order. Such equations have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics.

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