Nonlinear eigenvalue approximation

1988 ◽  
Vol 52 (4) ◽  
pp. 365-375 ◽  
Author(s):  
William F. Moss ◽  
Philip W. Smith ◽  
Joseph D. Ward
2010 ◽  
Vol 53 (1) ◽  
pp. 137-150 ◽  
Author(s):  
YiDu Yang ◽  
ZhiMin Zhang ◽  
FuBiao Lin

2003 ◽  
Vol 05 (05) ◽  
pp. 737-759 ◽  
Author(s):  
NOBUYOSHI FUKAGAI ◽  
KIMIAKI NARUKAWA

This paper deals with positive solutions of a class of nonlinear eigenvalue problems. For a quasilinear elliptic problem (#) - div (ϕ(|∇u|)∇u) = λf(x,u) in Ω, u = 0 on ∂Ω, we assume asymptotic conditions on ϕ and f such as ϕ(t) ~ tp0-2, f(x,t) ~ tq0-1as t → +0 and ϕ(t) ~ tp1-2, f(x,t) ~ tq1-1as t → ∞. The combined effects of sub-nonlinearity (p0> q0) and super-nonlinearity (p1< q1) with the subcritical term f(x,u) imply the existence of at least two positive solutions of (#) for 0 < λ < Λ.


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