Existence and multiplicity of sign-changing solutions for quasilinear Schr\"{o}dinger equations with sub-cubic nonlinearity.

In this paper, we consider the quasilinear Schrodinger equation \begin{equation*} -\Delta u+V(x)u-u\Delta(u^2)=g(u),\ \ x\in \mathbb{R}^{3}, \end{equation*} where $V$ and $g$ are continuous functions. Without the coercive condition on $V$ or the monotonicity condition on $g$, we show that the problem above has a least energy sign-changing solution and infinitely many sign-changing solutions. Our results especially solve the problem above in the case where $g(u)=|u|^{p-2}u$ ($2

Keywords:

• Physics
• Perturbation (astronomy)
• Schrödinger equation
• Mathematical physics
• Lemma (mathematics)
• Monotonic function
• Multiplicity (mathematics)
• Flow (mathematics)
• Invariant (mathematics)
• Energy (signal processing)

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