In this paper, by using variational approach, Mountain Pass Theorem and Krasnoselskii’s genus theory, we show the existence and multiplicity of solutions for a Schrödinger–Kirchhoff type equation involving the fractional \(p\left( .,.\right)\)-Laplacian in fractional Sobolev space with variable exponent. We also establish a Bartsch–Wang type compact embedding theorem for fractional Sobolev space with variable exponent.

中文翻译：

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带分数$$ p \ left（。，。\ right）$$ p。，的Schrödinger-Kirchhoff型方程的解的存在性和多重性。-$$ {\ mathbb {R}} ^ {N} $$ RN中的拉普拉斯算子

在本文中，我们使用变分方法，Mountain Pass定理和Krasnoselskii的属论，证明了包含分数\（p \ left（。，。\ right）\） -的Schrödinger-Kirchhoff型方程的解的存在性和多重性。分数Sobolev空间中具有可变指数的Laplacian。我们还为具有可变指数的分数Sobolev空间建立了Bartsch-Wang型紧致嵌入定理。