scholarly journals On the existence of positive solutions to a certain class of semilinear elliptic equations

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Norihisa Ikoma
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
Existence Of Positive Solutions

scholarly journals On positive solutions of some semilinear elliptic equations

1991 ◽  
Vol 50 (3) ◽  
pp. 343-355 ◽  
Author(s):  
Shin-Hwa Wang ◽  
Nicholas D. Kazarinoff
Keyword(s):  
Lower Bound ◽  
Existence Theorem ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Number Of Solutions ◽  
Nonexistence Theorem ◽  
Semilinear Elliptic ◽  
Existence Of Positive Solutions ◽  
Bound Theorem

AbstractThe 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.

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