Exact multiplicity of positive solutions for a class of semilinear equations on a ball

P. Korman, University of Cincinnati, Ohio, U.S.A.

E. J. Qualitative Theory of Diff. Equ., No. 8. (1999), pp. 1-15.

Abstract: We study exact multiplicity of positive solutions for a class of Dirichlet problems on a ball. We consider nonlinearities generalizing cubic, allowing both $f(0)=0$ and non-positone cases. We use bifurcation approach. We first prove our results for a special case, and then show that the global picture persists as we vary the roots.

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