Existence of solutions for perturbed fractional p-Laplacian equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:260

Article

Xiang, Mingqi¹  Zhang, Binlin²  Radulescu, Vicentiu D.^3,4 

[1] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

[2] Heilongjiang Inst Technol, Dept Math, Harbin 150050, Peoples R China

[3] King Abdulaziz Univ, Dept Math, Fac Sci, POB 80203, Jeddah 21589, Saudi Arabia

[4] Romanian Acad, Inst Math Simian Stoilow, POB 1-764, Bucharest 014700, Romania

关键词: Fractional p-Laplacian;    Fractional Schrodinger equation;    Mountain pass theorem;    Variational methods;   

DOI  :  10.1016/j.jde.2015.09.028

来源: Elsevier

【 摘 要 】

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: (-Delta)(p)(s)u + V (x)vertical bar u vertical bar(p-2)u = lambda a(x)vertical bar u vertical bar(r-2)u - b(x)vertical bar u vertical bar(q-2)u in R-N, where A is a real parameter, (-Delta)(p)(s) is the fractional p-Laplacian operator with 0 < s < 1 < p < infinity, p < r < min{q, p(s)*} and V, a, b : R-N -> (0, infinity) are three positive weights. Using variational methods, we obtain nonexistence and multiplicity results for the above-mentioned equations depending on lambda and according to the integrability properties of the ratio 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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