Abstract
We study the homogeneous Dirichlet boundary value problem of generalized Laplacian equations with a singular weight which may not be integrable. Some existence, multiplicity and nonexistence results of positive solutions under two different asymptotic behaviors of the nonlinearity at 0 and \(\infty \) are established in terms of different ranges of a parameter. Our approach is based on the fixed point theorem of expansion/compression of a cone and Schauder’s fixed point theorem.
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Acknowledgements
The first author was supported by the National Research Foundation of Korea, Grant funded by the Korea Government (MEST) (NRF2016R1D1A1B04931741).
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Communicated by Shangjiang Guo.
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Lee, YH., Xu, X. Existence and Multiplicity Results for Generalized Laplacian Problems with a Parameter. Bull. Malays. Math. Sci. Soc. 43, 403–424 (2020). https://doi.org/10.1007/s40840-018-0691-0
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DOI: https://doi.org/10.1007/s40840-018-0691-0