Multiple solutions for the fourth-order Kirchhoff type problems in $ \mathbb{R}^N $ involving concave-convex nonlinearities

Autor: Zijian Wu, Haibo Chen
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Electronic Research Archive, Vol 30, Iss 3, Pp 830-849 (2022)
Druh dokumentu: article
ISSN: 2688-1594
DOI: 10.3934/era.2022044?viewType=HTML
Popis: In this paper, we study the multiplicity of solutions for the following fourth-order Kirchhoff type problem involving concave-convex nonlinearities and indefinite weight function $ \begin{equation*} \Delta^2u-\left(a+b\int_{ \mathbb{R}^N}|\nabla u|^2dx\right)\Delta u+V(x)u = \lambda f(x)|u|^{q-2}u+|u|^{p-2}u, \end{equation*} $ where $ u\in H^2(\mathbb{R}^N)(4 < N < 8) $, $ \lambda > 0, 1 < q < 2, 4 < p < 2_\ast(2_\ast = 2N/(N-4)) $, $ f(x) $ satisfy suitable conditions, and $ f(x) $ may change sign in $ \mathbb{R}^N $. Using Nehari manifold and fibering maps, the existense of multiple solutions is established. Moreover, the existence of sign-changing solution is obtained for $ f(x)\equiv0 $. Our results generalize some recent results in the literature.
Databáze: Directory of Open Access Journals
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