Exact multiplicity for some nonlinear elliptic equations in balls

Wei, Juncheng

doi:10.1090/S0002-9939-97-04211-1

Exact multiplicity for some nonlinear elliptic equations in balls
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by Juncheng Wei

Proc. Amer. Math. Soc. 125 (1997), 3235-3242

DOI: https://doi.org/10.1090/S0002-9939-97-04211-1

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Abstract:

We present the exact multiplicity results for some nonlinear elliptic equations in balls of radius $R$. We prove that there is a critical value $R_{0}$ such that, for $R < R_{0}$, the equation has no solution; when $R=R_{0}$, it has exactly one solution; when $R > R_{0}$, it has exactly two solutions. Our main tool is the bifurcation theorem due to Crandall and Rabinowitz.

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