Global bifurcation of solutions of certain nonlinear eigenvalue problems for ordinary differential equations of fourth order

2016 ◽  
Vol 207 (12) ◽  
pp. 1625-1649 ◽  
Author(s):  
Z S Aliyev
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nonlinear Eigenvalue Problems ◽  
Bifurcation Of Solutions ◽  
Nonlinear Eigenvalue

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.

Nonlinear eigenvalue problems for a class of ordinary differential equations

2002 ◽  
Vol 132 (6) ◽  
pp. 1333-1359 ◽  
Author(s):  
Uri Elias ◽  
Allan Pinkus
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Eigenvalue Problems ◽  
Nonlinear Eigenvalue Problems ◽  
Various Boundary Conditions ◽  
Image Position ◽  
Nonlinear Eigenvalue

We consider the class of nonlinear eigenvalue problems where yp* = |y|p sgn y, pi > 0 and p0p1 … pn−1 = r, with various boundary conditions. We prove the existence of eigenvalues and study the zero properties and structure of the corresponding eigenfunctions.

scholarly journals Existence and bifurcation of solutions for Fredholm operators with nonlinear perturbations

1982 ◽  
Vol 86 ◽  
pp. 249-271 ◽  
Author(s):  
Yasuo Niikura
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Nonlinear Operator ◽  
Real Banach Space ◽  
Eigenvalue Problems ◽  
Nonlinear Perturbations ◽  
Fredholm Operators ◽  
Nonlinear Eigenvalue Problems ◽  
Bifurcation Of Solutions ◽  
Nonlinear Eigenvalue

In this paper we shall discuss nonlinear eigenvalue problems for the equations of the formwhere L is a linear operator on a real Banach space X with non-zero kernel, K(-) is a linear or nonlinear operator on X and M(·, ·) is an operator from X X R into X. Equations of the form (1) arise in various fields of physics and engineering.

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