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The set of positive solutions of semilinear equations in large balls. (English) Zbl 0625.35030
The exact number of positive classical solutions of $$\Delta u+f(u)=0$$ in $$B_ R$$, $$u=0$$ on $$\partial B_ R$$ is determined under appropriate assumptions on f. Solutions are classified into large and small solutions. For R sufficiently large, existence and uniqueness of small and large solutions are established, thus showing that there are exactly two positive (and radial) solutions. The results are obtained using the techniques of monotone separation of graphs to the linearized equations.
Reviewer: S.M.Lenhart

##### MSC:
 35J60 Nonlinear elliptic equations 35B32 Bifurcations in context of PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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##### References:
 [1] DOI: 10.1016/0022-0396(81)90077-2 · Zbl 0425.34028 [2] DOI: 10.1016/0022-0396(86)90112-9 · Zbl 0577.35035 [3] DOI: 10.1007/BF00250651 · Zbl 0516.35031 [4] DOI: 10.1007/BF01455933 · Zbl 0576.35044 [5] DOI: 10.1512/iumj.1981.30.30012 · Zbl 0522.35036 [6] DOI: 10.1007/BF00279955 · Zbl 0606.35029 [7] Gidas, Adv. in Math. Suppl. Stud. 7A pp 369– (1981)
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