We consider quasilinear elliptic equations, including the following Modified Nonlinear Schrödinger Equation as a special example:

$ \begin{equation*} \left\{ \begin{aligned} &\Delta u+\frac{1}{2}u\Delta u^2+\lambda |u|^{r-2}u = 0, \ \ \ \text{in}\,\,\Omega,\\ &u = 0\quad\text{on}\,\,\partial\Omega, \end{aligned} \right. \end{equation*} $

中文翻译：

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参数相关的拟线性方程组的符号转换解

我们考虑准线性椭圆方程，包括以下修改的非线性薛定ding方程作为一个特殊示例：

$ \ begin {equation *} \ left \ {\ begin {aligned}＆\ Delta u + \ frac {1} {2} u \ Delta u ^ 2 + \ lambda | u | ^ {r-2} u = 0， \ \ \ \ text {in} \，\，\ Omega，\\＆u = 0 \ quad \ text {on} \，\，\ partial \ Omega，\ end {aligned} \ right。\ end {equation *} $