Nonlinear eigenvalue approximation

1988 ◽  
Vol 52 (4) ◽  
pp. 365-375 ◽  
Author(s):  
William F. Moss ◽  
Philip W. Smith ◽  
Joseph D. Ward
Keyword(s):  
Eigenvalue Approximation ◽  
Nonlinear Eigenvalue

Eigenvalue approximation from below using non-conforming finite elements

2010 ◽  
Vol 53 (1) ◽  
pp. 137-150 ◽  
Author(s):  
YiDu Yang ◽  
ZhiMin Zhang ◽  
FuBiao Lin
Keyword(s):  
Finite Elements ◽  
Eigenvalue Approximation

MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORS

2003 ◽  
Vol 05 (05) ◽  
pp. 737-759 ◽  
Author(s):  
NOBUYOSHI FUKAGAI ◽  
KIMIAKI NARUKAWA
Keyword(s):  
Positive Solutions ◽  
Elliptic Problem ◽  
Eigenvalue Problems ◽  
Multiple Positive Solutions ◽  
Combined Effects ◽  
Nonlinear Eigenvalue Problems ◽  
Quasilinear Elliptic Problem ◽  
Quasilinear Elliptic ◽  
Nonlinear Eigenvalue

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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