Finer analysis of the Nehari set associated to a class of Kirchhoff-type equations

Kaye Silva () and Steffânio M. Sousa ()
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Kaye Silva: Universidade Federal de Goiás
Steffânio M. Sousa: Universidade Federal de Goiás

Partial Differential Equations and Applications, 2020, vol. 1, issue 6, 1-23

Abstract: Abstract We extend and improve the results of Chen-Ou (Comput. Math. Appl. 77(10):2859–2866, 2019), which concern a Kirchhoff-type equation depending on two real parameters $$\lambda ,\mu$$ λ , μ . Our technique, which relies upon a refined analysis of the Nehari set associated to the problem, permit us prove existence and multiplicity of solutions by minimizing the associated energy functional over components of the Nehari set. We also analyze the threshold of the method and prove existence of solutions even in the case where the Nehari set is not a manifold.

Keywords: Nehari manifold; Variational methods; Extremal parameter; Kirchhoff; Bifurcation; Young modulus; 35A02; 35A15; 35B32 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s42985-020-00046-8

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