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On non-local nonlinear elliptic equations involving an eigenvalue problem

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The existence and multiplicity of solutions for a class of non-local elliptic boundary value problems with superlinear source functions are investigated in this paper. Using variational methods, we examine the changes arise in the solution behaviors as a result of the non-local effect. Comparisons are made of the results here with those of the elliptic boundary value problem in the absence of the non-local term under the same prescribed conditions to highlight this effect of non-locality on the solution behaviors. Our results here demonstrate that the complexity of the solution structures is significantly increased in the presence of the non-local effect with the possibility ranging from no permissible positive solution to three positive solutions and, contrary to those obtained in the absence of the non-local term, the solution profiles also vary depending on the superlinearity of the source functions.

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Acknowledgements

K.-H Wang was supported in part by the Ministry of Science and Technology, Taiwan (Grant No. 108-2811-M-390-500) and T.-F. Wu was supported in part by the Ministry of Science and Technology, Taiwan (Grant No. 108-2115-M-390-007-MY2).

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Authors and Affiliations

  1. Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, 811, Taiwan

    Ching-yu Chen, Yueh-cheng Kuo, Kuan-Hsiang Wang & Tsung-fang Wu

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  1. Ching-yu Chen
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  2. Yueh-cheng Kuo
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  3. Kuan-Hsiang Wang
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  4. Tsung-fang Wu
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Correspondence to Tsung-fang Wu.

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Chen, Cy., Kuo, Yc., Wang, KH. et al. On non-local nonlinear elliptic equations involving an eigenvalue problem. RACSAM 116, 45 (2022). https://doi.org/10.1007/s13398-021-01190-5

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