scholarly journals A projection method for nonlinear eigenvalue problems using contour integrals

JSIAM Letters ◽  
2013 ◽  
Vol 5 (0) ◽  
pp. 41-44 ◽  
Author(s):  
Shinnosuke Yokota ◽  
Tetsuya Sakurai
Keyword(s):  
Projection Method ◽  
Eigenvalue Problems ◽  
Nonlinear Eigenvalue Problems ◽  
Contour Integrals ◽  
Nonlinear Eigenvalue

scholarly journals A numerical method for nonlinear eigenvalue problems using contour integrals

JSIAM Letters ◽  
2009 ◽  
Vol 1 (0) ◽  
pp. 52-55 ◽  
Author(s):  
Junko Asakura ◽  
Tetsuya Sakurai ◽  
Hiroto Tadano ◽  
Tsutomu Ikegami ◽  
Kinji Kimura
Keyword(s):  
Numerical Method ◽  
Eigenvalue Problems ◽  
Nonlinear Eigenvalue Problems ◽  
Contour Integrals ◽  
Nonlinear Eigenvalue

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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