Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity
Asymptotic Analysis(2024)
Abstract
We are concerned with solutions of the following quasilinear Schrödinger
equations
-div(φ^2(u) ∇
u)+φ(u) φ^'(u)|∇ u|^2+λ u=f(u), x
∈ℝ^N
with prescribed mass
∫_ℝ^N u^2dx=c,
where N≥ 3, c>0, λ∈ℝ appears as the Lagrange multiplier and φ∈ C
^1(ℝ ,ℝ^+). The nonlinearity f ∈ C ( ℝ,
ℝ ) is allowed to be mass-subcritical, mass-critical and
mass-supercritical at origin and infinity. Via a dual approach, the fixed point
index and a global branch approach, we establish the existence of normalized
solutions to the problem above. The results extend previous results by L.
Jeanjean, J. J. Zhang and X.X. Zhong to the quasilinear case.
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