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Asymptotic oscillations of global solution branches for nonlinear problems

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In this paper we first study the asymptotic oscillations of a connected component of the positive solution set of some non-positone operator equations using global bifurcation theories. Then by using these results, we study the asymptotic oscillations of a connected component of the positive solution set of some differential boundary value problems. This paper extends some previous results on asymptotic oscillations of a connected component of the positive solution set of differential boundary value problems to the operator equations in real Banach spaces and includes a more general boundary condition. The existence of infinitely many solutions can also be obtained by using our main results.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, People’s Republic of China

    Xian Xu, Li Sun & Zhen Wang

  2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    Donal O’Regan

Authors
  1. Xian Xu
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  2. Li Sun
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  3. Donal O’Regan
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  4. Zhen Wang
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Correspondence to Li Sun.

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This work was supported by the National Nature Science Foundation of China (Grant Nos. NSFC11501260, NSFC11571146, NSFC10971179, NSFC11026203, NSFC11071205), the Na ture Science Foundation of Jiangsu Province (Grant No. BK2011202), the Natural Science Foundation of Jiangsu Education Committee (Grant No. 09KJB110008) and Qing Lan Project, the Priority Academic Program Development (PAPD) and Top-notch Academic Programs Project (TAPP) of Jiangsu Higher Education Institutions (PPZY2015A013)

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Xu, X., Sun, L., O’Regan, D. et al. Asymptotic oscillations of global solution branches for nonlinear problems. Positivity 25, 1511–1541 (2021). https://doi.org/10.1007/s11117-021-00826-5

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