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Existence and multiplicity of solutions for nonlocal systems with Kirchhoff type

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arxiv 1410.6225 v1 pith:I47EEN4B submitted 2014-10-23 math.AP

Zhitao Zhang , Yimin Sun This is my paper · ORCID
classification math.AP
keywords existencekirchhoffmultiplicitynonlocalpositiveproveresultsolutions
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abstract

Firstly, we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type. Then a multiplicity result is established by cohomological index of Fadell and Rabinowitz. We also consider the critical case and prove existence of positive least energy solution when the parameter $\beta$ is sufficiently large.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An iterative method for Kirchhoff type equations and its applications

    math.AP 2019-08 reject novelty 6.0 of 10

    An invariant-set existence theorem for nonlocal Kirchhoff-Carrier equations is asserted, but the proof rests on a false identity for r_M and an invalid gradient bound.

  2. Positive solutions of inhomogeneous Kirchhoff type equations with indefinite data

    math.AP 2019-08 conditional novelty 5.0 of 10

    For a Kirchhoff equation with indefinite data, the paper characterizes positive solvability through an auxiliary linear problem, showing existence, multiplicity, uniqueness, and nonexistence depending on the exponent ...

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