In this paper, we construct sign-changing radial solutions for a class of Schrödinger equations with saturable nonlinearity which arises from several models in mathematical physics. More precisely, for any given nonnegative integer k, by using a minimization argument, we first obtain a sign-changing minimizer with k nodes of a constrained minimization problem, and show, by a deformation lemma and Miranda’s theorem, that the minimizer is the desired solution.

中文翻译：

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具有饱和非线性的一类Schrödinger方程的多重符号转换解

在本文中，我们为一类具有饱和非线性的Schrödinger方程构造符号变换径向解，这是由数学物理中的多个模型引起的。更确切地说，对于任何给定的非负整数k，通过使用最小化参数，我们首先获得带有约束最小化问题的k个节点的符号变化最小化器，并通过变形引理和Miranda定理表明，最小化器是期望的解。