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.
Existence and multiplicity of solutions for nonlocal systems with Kirchhoff type
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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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2019 1verdicts
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An iterative method for Kirchhoff type equations and its applications
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.