We consider the following parametric double-phase problem: . We do not impose any global growth conditions to the nonlinearity , which refer solely to its behavior in a neighborhood of . And we will show that they suffice for the multiplicity of signed and nodal solutions of the double-phase problem above when is large enough.

中文翻译：

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一类双阶段问题的多重节点解

我们考虑以下参数双相问题： 。我们不对非线性施加任何全球增长条件，仅指其在以下地区的行为。并且我们将证明它们足够大时满足上述双相问题的有符号和节点解的多重性。