Two Parameter Eigenvalue Problems in Ordinary Differential Equations (M. Faierman)

SIAM Review ◽  
1992 ◽  
Vol 34 (4) ◽  
pp. 684-687
Author(s):  
B. D. Sleeman
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Eigenvalue Problems ◽  
Two Parameter

An eigenfunction expansion associated with a two-parameter system of differential equations. III

1983 ◽  
Vol 93 (3-4) ◽  
pp. 189-195 ◽  
Author(s):  
M. Faierman
Keyword(s):  
Differential Equations ◽  
Uniform Convergence ◽  
Ordinary Differential Equations ◽  
Eigenfunction Expansion ◽  
Second Order ◽  
System Of Differential Equations ◽  
Parameter System ◽  
Two Parameter

SynopsisWe continue with the work of earlier papers concerning the use of partial dilferential equations to prove the uniform convergence of the eigenfunction expansion associated witha left definite two-parameter system of ordinary differential equations of the second order.

scholarly journals Global Bifurcation of Fourth-Order Nonlinear Eigenvalue Problems’ Solution

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Fatma Aydin Akgun
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nonlinear Eigenvalue Problems ◽  
Nodal Properties ◽  
Nonlinear Eigenvalue

In this paper, we study the global bifurcation of infinity of a class of nonlinear eigenvalue problems for fourth-order ordinary differential equations with nondifferentiable nonlinearity. We prove the existence of two families of unbounded continuance of solutions bifurcating at infinity and corresponding to the usual nodal properties near bifurcation intervals.

The interlacing of eigenvalues for periodic multi-parameter problems

1978 ◽  
Vol 80 (3-4) ◽  
pp. 357-362 ◽  
Author(s):  
Patrick J. Browne
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Image Position ◽  
Periodic Equation

SynopsisThis paper studies a linked system of second order ordinary differential equationswhere xx ∈ [ar, br] and the coefficients qrars are continuous, real valued and periodic of period (br − ar), 1 ≤ r,s ≤ k. We assume the definiteness condition det{ars(xr)} > 0 and 2k possible multiparameter eigenvalue problems are then formulated according as periodic or semi-periodic boundary conditions are imposed on each of the equations of (*). The main result describes the interlacing of the 2k possible sets of eigentuples thus extending to the multiparameter case the well known theorem concerning 1-parameter periodic equation.

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