In this paper we obtain the existence of nontrivial solutions for the fractional Laplacian equations with the nonlinearity may fail to have asymptotic limits at zero and at infinity. We make use of a combination of homotopy invariance of critical groups and the topological version of linking methods.

中文翻译：

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在无穷大和零附近没有渐近极限的分数拉普拉斯问题的非平凡解

在本文中，我们获得了具有非线性的分数拉普拉斯方程的非平凡解的存在性可能在零和无穷远处不具有渐近极限。我们结合使用关键群的同伦不变性和链接方法的拓扑版本。