abstract
The structure of the set of positive solutions of the semilinear elliptic boundary value problem \(\Delta u(x)+\lambda f(u(x))=0\ \ \ {\rm for}\ x\in D,\ \ \ u=0\ \ {\rm on}\ \partial D\) depends on a certain non-degeneracy condition, which was proved by K.J. Brown [1] and T. Ouyang and J. Shi [5]. We provide a short alternative proof of that condition.
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References
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T. Ouyang and J. Shi, Exact multiplicity of positive solutions for a class of semilinear problems. J. Differential Equations 146, 121–156 (1998).
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Supported in part by the Taft Faculty Grant at the University of Cincinnati
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Korman, P. A remark on the non-degeneracy condition. Results. Math. 41, 334–336 (2002). https://doi.org/10.1007/BF03322775
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DOI: https://doi.org/10.1007/BF03322775