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On the structure of positive solutions to an elliptic problem arising in thin film equations
Journal article   Open access   Peer reviewed

On the structure of positive solutions to an elliptic problem arising in thin film equations

Peng Feng
Journal of mathematical analysis and applications, Vol.370(2), pp.573-583
2010
DOI: https://doi.org/10.1016/j.jmaa.2010.04.049

Abstract

Radial solution Singular elliptic equation Thin film equation
We consider the structure of positive radial solutions of Δ u + u − α − u − β = 0 in B R , u = 0 on ∂ B R , where B R is a ball in R N with radius R. When 0 < α < β < 1 , we show that there exists R ∗ > 0 such that when R > R ∗ , the Dirichlet problem has exactly two radial solutions; when R = R ∗ , the solution is unique and there is no solution for R < R ∗ . When 0 < β < α < 1 , we show that for any R > 0 , the radial solution exists and is unique.
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https://doi.org/10.1016/j.jmaa.2010.04.049View
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