Fractional p-Laplacian Equations with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition



The main purpose of this paper is to investigate the existence of nontrivial solutions to a class of quasilinear non-local problems which do not satisfy the Ambrosetti–Rabinowitz (AR) condition where the nonlinear terms are superlinear at 0 and of subcritical or critical exponential growth (subcritical polynomial growth) at \(\infty \). Some existence results for nontrivial solution are obtained using mountain pass theorem combined with the fractional Moser–Trudinger inequality.


Fractional p-Laplacian problems subcritical or critical exponential growth mountain pass theorem without the (AR)condition 

Mathematics Subject Classification

35A15 35J92 46E30 



This research is supported by the NSFC (Nos. 11661070, 11764035 and 11571176).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTianshui Normal UniversityTianshuiPeople’s Republic of China

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