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Positive solutions for a class of biharmonic problems: existence, nonexistence and multiplicity

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Abstract

The main objective of this article is to consider a biharmonic problem with Navier boundary conditions. Among others, some criteria for the existence, multiplicity and nonexistence of positive solutions are established by employed fixed point theorems in a cone. In addition, we not only consider the sublinear case, but also we will study the case of appropriate combinations of superlinearity and sublinearity.

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Acknowledgements

This work is sponsored by the Beijing Natural Science Foundation (1212003). The author is grateful to anonymous referees for their constructive comments and suggestions, which has greatly improved this paper.

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Authors and Affiliations

  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, People’s Republic of China

    Meiqiang Feng

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  1. Meiqiang Feng
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Correspondence to Meiqiang Feng.

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Communicated by Klaus Guerlebeck.

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Feng, M. Positive solutions for a class of biharmonic problems: existence, nonexistence and multiplicity. Ann. Funct. Anal. 14, 30 (2023). https://doi.org/10.1007/s43034-023-00254-4

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  • DOI: https://doi.org/10.1007/s43034-023-00254-4

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