文章基本信息

标题：Nontrivial Solution for the Fractional -Laplacian Equations via Perturbation Methods
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作者：Huxiao Luo ; Shengjun Li ; Xianhua Tang 等
期刊名称：Advances in Mathematical Physics
印刷版ISSN：1687-9120
电子版ISSN：1687-9139
出版年度：2017
卷号：2017
DOI：10.1155/2017/5317213
出版社：Hindawi Publishing Corporation
摘要：We study the existence of nontrivial solution of the following equation without compactness: , where , , is the fractional -Laplacian, and the subcritical -superlinear term is 1-periodic in for . Our main difficulty is that the weak limit of (PS) sequence is not always the weak solution of fractional -Laplacian type equation. To overcome this difficulty, by adding coercive potential term and using mountain pass theorem, we get the weak solution of perturbation equations. And we prove that as . Finally, by using vanishing lemma and periodic condition, we get that is a nontrivial solution of fractional -Laplacian equation.