On the solvability of an indefinite nonlinear Kirchhoff equation via associated eigenvalue problems

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Zhang, Han-Su¹  Li, Tiexiang¹  Wu, Tsung-fang² 

[1] Southeast Univ, Sch Math, Nanjing 211189, Peoples R China

[2] Natl Univ Kaohsiung, Dept Appl Math, Kaohsiung 811, Taiwan

关键词: Nonlinear Kirchhoff equations;    Nehari manifold;    Eigenvalue problem;    Positive solution;    Concentration-compactness principle;   

DOI  :  10.1016/j.jde.2020.02.017

来源: Elsevier

【 摘 要 】

We study the non-existence, existence and multiplicity of positive solutions to the following nonlinear Kirchhoff equation: where N(t)= at+ b(a, b> 0), the potential Vis a nonnegative function in R-N and the weight function Q is an element of L-infinity (RN) with changes sign in Omega :={V= 0}. We mainly prove the existence of at least two positive solutions in the cases that (i) 2 < p< min { 4,2*} and near for mu > 0 sufficiently where lambda(1) (f(Omega)) is the first eigenvalue of - Delta in H with weight function f whose corresponding positive principal eigenfunction is denoted by phi(1). Furthermore, we also investigated the non-existence and existence of positive solutions if a,.belongs to different intervals. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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