scholarly journals Spectral properties of a Fourth-Order eigenvalue problem with quadratic spectral parameters in a boundary condition

2020 ◽  
Vol 5 (2) ◽  
pp. 904-922
Author(s):  
Chenghua Gao ◽  
◽  
Maojun Ran
Keyword(s):  
Boundary Condition ◽  
Eigenvalue Problem ◽  
Fourth Order ◽  
Spectral Properties ◽  
Spectral Parameters ◽  
Fourth Order Eigenvalue Problem

scholarly journals Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Hua Luo ◽  
Chenghua Gao
Keyword(s):  
Fixed Point ◽  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Solution Method ◽  
Lower Solution ◽  
Existence Results ◽  
Fourth Order Eigenvalue Problem ◽  
Existence And Nonexistence ◽  
Lower Solution Method

LetTbe a time scale anda,b∈T,a<ρ2(b). We study the nonlinear fourth-order eigenvalue problem onT,uΔ4(t)=λh(t)f(u(t),uΔ2(t)),t∈[a,ρ2(b)]T,u(a)=uΔ(σ(b))=uΔ2(a)=uΔ3(ρ(b))=0and obtain the existence and nonexistence of positive solutions when0<λ≤λ*andλ>λ*, respectively, for someλ*. The main tools to prove the existence results are the Schauder fixed point theorem and the upper and lower solution method.

C0IPG for a Fourth Order Eigenvalue Problem

2016 ◽  
Vol 19 (2) ◽  
pp. 393-410 ◽  
Author(s):  
Xia Ji ◽  
Hongrui Geng ◽  
Jiguang Sun ◽  
Liwei Xu
Keyword(s):  
Eigenvalue Problem ◽  
Galerkin Method ◽  
Numerical Computation ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Fourth Order ◽  
Well Posedness ◽  
Numerical Examples ◽  
Fourth Order Eigenvalue Problem ◽  
Lagrange Elements

AbstractThis paper concerns numerical computation of a fourth order eigenvalue problem. We first show the well-posedness of the source problem. An interior penalty discontinuous Galerkin method (C0IPG) using Lagrange elements is proposed and its convergence is studied. The method is then used to compute the eigenvalues. We show that the method is spectrally correct and prove the optimal convergence. Numerical examples are presented to validate the theory.

scholarly journals Spectral properties of a fourth order eigenvalue problem with spectral parameter in the boundary conditions

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2421-2431
Author(s):  
Ziyatkhan Aliyev ◽  
Sevinc Guliyeva
Keyword(s):  
Eigenvalue Problem ◽  
Fourth Order ◽  
Cross Sections ◽  
Inertial Mass ◽  
Longitudinal Force ◽  
Order Ordinary Differential Equation ◽  
Bending Vibrations ◽  
Fourth Order Eigenvalue Problem ◽  
The Right ◽  
Oscillation Properties

In this paper we consider the eigenvalue problem for fourth order ordinary differential equation that describes the bending vibrations of a homogeneous rod, in cross-sections of which the longitudinal force acts, the left end of which is fixed rigidly and on the right end an inertial mass is concentrated. We characterize the location of the eigenvalues on the real axis, we investigate the structure of root spaces and oscillation properties of eigenfunctions and their derivatives, we study the basis properties in the space Lp, 1 < p < ?, of the system of eigenfunctions of considered problem.

Some global results for nonlinear fourth order eigenvalue problems

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Ziyatkhan Aliyev
Keyword(s):  
Eigenvalue Problem ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nontrivial Solutions ◽  
Fourth Order Eigenvalue Problem

AbstractIn this paper, we consider the nonlinear fourth order eigenvalue problem. We show the existence of family of unbounded continua of nontrivial solutions bifurcating from the line of trivial solutions. These global continua have properties similar to those found in Rabinowitz and Berestycki well-known global bifurcation theorems.

Sign in / Sign up

Export Citation Format

Share Document