Variational Methods for Multiparametric Eigenvalue Problems

1977 ◽  
pp. 119-132 ◽  
Author(s):  
G. F. Roach
Keyword(s):  
Variational Methods ◽  
Eigenvalue Problems

scholarly journals Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications

2021 ◽  
Vol 41 (4) ◽  
pp. 489-507
Author(s):  
Abdelrachid El Amrouss ◽  
Omar Hammouti
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Critical Point Theory ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Difference Operator ◽  
Periodic Boundary Conditions ◽  
Point Theory ◽  
Existence Of A Solution ◽  
Order Difference

Let \(n\in\mathbb{N}^{*}\), and \(N\geq n\) be an integer. We study the spectrum of discrete linear \(2n\)-th order eigenvalue problems \[\begin{cases}\sum_{k=0}^{n}(-1)^{k}\Delta^{2k}u(t-k) = \lambda u(t) ,\quad & t\in[1, N]_{\mathbb{Z}}, \\ \Delta^{i}u(-(n-1))=\Delta^{i}u(N-(n-1)),\quad & i\in[0, 2n-1]_{\mathbb{Z}},\end{cases}\] where \(\lambda\) is a parameter. As an application of this spectrum result, we show the existence of a solution of discrete nonlinear \(2n\)-th order problems by applying the variational methods and critical point theory.

scholarly journals EIGENVALUE PROBLEMS FOR SINGULAR ODES

2010 ◽  
Vol 53 (2) ◽  
pp. 301-312 ◽  
Author(s):  
DONAL O'REGAN ◽  
ALEKSANDRA ORPEL
Keyword(s):  
Dirichlet Problem ◽  
Variational Methods ◽  
Continuous Dependence ◽  
Eigenvalue Problems ◽  
Functional Parameters ◽  
Eigenvalue Intervals ◽  
Continuous Dependence Of Solutions ◽  
Singular Odes

AbstractWe investigate eigenvalue intervals for the Dirichlet problem when the nonlinearity may be singular at t = 0 or t = 1. Our approach is based on variational methods and cover both sublinear and superlinear cases. We also study the continuous dependence of solutions on functional parameters.

Generalized Prüfer Angle and Variational Methods for p-Laplacian Eigenvalue Problems on the Half-Line

2008 ◽  
Vol 51 (3) ◽  
pp. 565-579 ◽  
Author(s):  
Paul Binding ◽  
Patrick J. Browne
Keyword(s):  
Eigenvalue Problem ◽  
Variational Methods ◽  
Eigenvalue Problems ◽  
Variational Principles ◽  
Nonlinear Eigenvalue Problem ◽  
Half Line ◽  
Laplacian Eigenvalue ◽  
Prüfer Angle ◽  
Image Position ◽  
And Variational Principles

AbstractThe nonlinear eigenvalue problemfor 0 ≤ x < ∞, fixed p ∈ (1, ∞), and with y′(0)/y(0) specified, is studied under conditions on q related to those of Brinck and Molanov. Topics include Sturmian results, connections between problems on finite intervals and the half-line, and variational principles.

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