Existence and Multiplicity of Positive Radial Solutions for Semilinear Elliptic Equations in Annular Domains | Zendy

Song-Sun Lin | Zendy; Feng Ming Pai | Zendy

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Existence and Multiplicity of Positive Radial Solutions for Semilinear Elliptic Equations in Annular Domains

Author(s) -

Song-Sun Lin,

Feng Ming Pai

Publication year - 1991

Publication title -

siam journal on mathematical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.882

H-Index - 92

eISSN - 1095-7154

pISSN - 0036-1410

DOI - 10.1137/0522097

Subject(s) - multiplicity (mathematics) , mathematics , mathematical analysis , elliptic curve , pure mathematics , mathematical physics

The existence and multiplicity of positive radial solutions of equation Au +f(u) 0 is studied in annular domains in Rn, n >_- 2. It is proven that iff(0) >_- 0,f is somewhere negative in (0,) and superlinear at, then there is a large positive radial solutions on all annuli. Iff(0)< 0 and satisfies certain conditions, then the equation has no solution if the annuli are too wide. Multiplicity results are also obtained when f has many humps with positive areas.

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