Asymptotically linear fractional p-Laplacian equations

被引：0
作者：
Rossella Bartolo
Giovanni Molica Bisci
机构：
[1] Politecnico di Bari,Dipartimento di Meccanica, Matematica e Management
[2] Università ‘Mediterranea’ di Reggio Calabria,Dipartimento PAU
来源：
Annali di Matematica Pura ed Applicata (1923 -) | 2017年 / 196卷
关键词：
Fractional ; -Laplacian; Integro-differential operator; Variational methods; Asymptotically linear problem; Resonant problem; Pseudo-genus; Primary 49J35; 35A15; 35S15; 58E05; Secondary 47G20; 45G05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we study the multiplicity of weak solutions to (possibly resonant) nonlocal equations involving the fractional p-Laplacian operator. More precisely, we consider a Dirichlet problem driven by the fractional p-Laplacian operator and involving a subcritical nonlinear term which does not satisfy the technical Ambrosetti–Rabinowitz condition. By framing this problem in an appropriate variational setting, we prove a multiplicity theorem.
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页码：427 / 442
页数：15
相关论文
共 53 条
[1]  
Bartolo P(1983)Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity Nonlinear Anal. 7 981-1012
[2]  
Benci V(2013)-Laplacian problems with nonlinearities interacting with the spectrum Nonlinear Differ. Equ. Appl. 20 1701-1721
[3]  
Fortunato D(1982)On the critical point theory for indefinite functionals in the presence of symmetries Trans. Am. Math. Soc. 274 533-572
[4]  
Bartolo R(2015)Superlinear nonlocal fractional problems with infinitely many solutions Nonlinearity 28 2247-2264
[5]  
Candela AM(1993)A deformation lemma on a Manuscr. Math. 81 339-359
[6]  
Salvatore A(2010) manifold Adv. Math. 224 2052-2093
[7]  
Benci V(2007)Positive solutions of nonlinear problems involving the square root of the Laplacian Commun. Partial Differ. Equ. 32 1245-1260
[8]  
Binlin Z(2009)An extension problem related to the fractional Laplacian Commun. Pure Appl. Math. 62 597-638
[9]  
Molica Bisci G(2011)Regularity theory for fully nonlinear integro-differential equations Arch. Ration. Mech. Anal. 200 59-88
[10]  
Servadei R(2009)Regularity results for nonlocal equations by approximation Calc. Var. Partial Differ. Equ. 34 495-530
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