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On positive solutions of some semilinear elliptic equations

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

Shin-Hwa Wang  and
Nicholas D. Kazarinoff
Shin-Hwa Wang
Affiliation:
Department of Mathematics National Tsing Hua UniversityHsinchuTaiwan300, R.O.C.
Nicholas D. Kazarinoff
Affiliation:
Department of Mathematics State University of New YorkBuffalo, New York, 14214-3093, U.S.A.
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Abstract

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The existence of positive solutions of some semilinear elliptic equations of the form −Δu = λf(u) is studied. The major results are a nonexistence theorem which gives a λ* = λ*(f,Ω) > 0 below which no positive solutions exist and a lower bound theorem for umax for Ω a ball. As a corollary of the nonexistence theorem that describes the dependence of the number of solutions on λ, two other nonexistence theorems, and an existence theorem are also proved.

Keywords

positive solutionsemilinear elliptic equationdegree theory

MSC classification

Secondary: 35J65: Nonlinear boundary value problems for linear elliptic equations 35J25: Boundary value problems for second-order elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 3 , June 1991 , pp. 343 - 355
Copyright
Copyright © Australian Mathematical Society 1991

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