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Multiple Solutions for a Class of New p(x)-Kirchhoff Problem without the Ambrosetti-Rabinowitz Conditions

College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
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Mathematics 2020, 8(11), 2068; https://doi.org/10.3390/math8112068
Received: 19 October 2020 / Revised: 13 November 2020 / Accepted: 16 November 2020 / Published: 19 November 2020
(This article belongs to the Special Issue New Trends in Variational Methods in Nonlinear Analysis)
In this paper, we consider a nonlocal p(x)-Kirchhoff problem with a p+-superlinear subcritical Caratheodory reaction term, which does not satisfy the Ambrosetti–Rabinowitz condition. Under some certain assumptions, we prove the existence of nontrivial solutions and many solutions. Our results are an improvement and generalization of the corresponding results obtained by Hamdani et al. (2020). View Full-Text
Keywords: variable exponent; nonlocal Kirchhoff equation; variational method; existence of nontrivial solutions; multiple solutions; fountain theorem; dual fountain theorem variable exponent; nonlocal Kirchhoff equation; variational method; existence of nontrivial solutions; multiple solutions; fountain theorem; dual fountain theorem
MDPI and ACS Style

Zhang, B.-L.; Ge, B.; Cao, X.-F. Multiple Solutions for a Class of New p(x)-Kirchhoff Problem without the Ambrosetti-Rabinowitz Conditions. Mathematics 2020, 8, 2068. https://doi.org/10.3390/math8112068

AMA Style

Zhang B-L, Ge B, Cao X-F. Multiple Solutions for a Class of New p(x)-Kirchhoff Problem without the Ambrosetti-Rabinowitz Conditions. Mathematics. 2020; 8(11):2068. https://doi.org/10.3390/math8112068

Chicago/Turabian Style

Zhang, Bei-Lei; Ge, Bin; Cao, Xiao-Feng. 2020. "Multiple Solutions for a Class of New p(x)-Kirchhoff Problem without the Ambrosetti-Rabinowitz Conditions" Mathematics 8, no. 11: 2068. https://doi.org/10.3390/math8112068

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