Existence of solutions for perturbed fractional p-Laplacian equations

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• 作者：Mingqi Xiang^a ; ^{xiangmingqi_hit@163.com" class="auth_mail" title="E-mail the corresponding author} ; Binlin Zhang^b ; ^{zhangbinlin2012@163.com" class="auth_mail" title="E-mail the corresponding author} ; Vicenţiu D. Rădulescu^c ; ^d ; ^{vicentiu.radulescu@imar.ro" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35R11 ; 35A15 ; 35J60 ; 47G20
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：260
• 期：2
• 页码：1392-1413
• 全文大小：331 K

文摘

The purpose of this paper is to investigate the existence of weak solutions for a perturbed nonlinear elliptic equation driven by the fractional p-Laplacian operator as follows: where λ   is a real parameter, ${(-\mathrm{\Delta })}_p^s$ is the fractional p  -Laplacian operator with 0<s<1<p<∞$0<s<1<p<\infty$, $p<r<\min \{q,p_s^{⁎}\}$ and V,a,b:R^N→(0,∞)$V,a,b:{\mathbb{R}}^N\to (0,\infty )$ are three positive weights. Using variational methods, we obtain nonexistence and multiplicity results for the above-mentioned equations depending on λ   and according to the integrability properties of the ratio a^q−p/b^r−p$a^{q-p}/b^{r-p}$. Our results extend the previous work of Autuori and Pucci (2013) [5] to the fractional p-Laplacian setting. Furthermore, we weaken one of the conditions used in their paper. Hence the results of this paper are new even in the fractional Laplacian case.