scholarly journals Limit-Point/Limit-Circle Results for Superlinear Damped Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
M. Bartušek ◽  
John R. Graef
Keyword(s):  
Differential Equations ◽  
Limit Point ◽  
Second Order ◽  
Limit Circle

The authors study the nonlinear limit-point and limit-circle properties for second-order nonlinear damped differential equations of the form(a(t)|y'|p-1y')'+b(t)|y'|q-1y'+r(t)|y|λ-1y=0,where0<q≤p≤λ,a(t)>0, andr(t)>0. Examples to illustrate the main results are included.

scholarly journals Limit Circle/Limit Point Criteria for Second-Order Superlinear Differential Equations with a Damping Term

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Lihong Xing ◽  
Wei Song ◽  
Zhengqiang Zhang ◽  
Qiyi Xu
Keyword(s):  
Differential Equations ◽  
Limit Point ◽  
Second Order ◽  
Damping Term ◽  
Limit Circle ◽  
New Criteria ◽  
Point Type ◽  
Circle Limit

The purpose of the present paper is to establish some new criteria for the classifications of superlinear differential equations as being of the nonlinear limit circle type or of the nonlinear limit point type. The criteria presented here generalize some known results in literature.

scholarly journals Limit Circle/Limit Point Criteria for Second-Order Sublinear Differential Equations with Damping Term

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Jing Shao ◽  
Wei Song
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Limit Point ◽  
Second Order ◽  
Damping Term ◽  
Limit Circle ◽  
New Criteria ◽  
Point Type ◽  
Circle Limit

The purpose of the present paper is to establish some new criteria for the classification of the sublinear differential equation as of the nonlinear limit circle type or of the nonlinear limit point type. The criteria presented here generalize some known results in the literature.

20.—On the Limit-point and Limit-circle Theory of Second-order Differential Equations

1975 ◽  
Vol 72 (3) ◽  
pp. 245-256
Author(s):  
K. S. Ong
Keyword(s):  
Differential Equations ◽  
Weight Function ◽  
Limit Point ◽  
Circle Method ◽  
Second Order ◽  
Limit Circle ◽  
Second Order Differential Equations

SynopsisIn this paper the Weyl limit-point and limit-circle theory of second-order differential equations is extended to the case that the weight function is allowed to take on both positive and negative values—the polar case. This extension is achieved using Weyl's limit circle method.

scholarly journals Limit-Point/Limit-Circle Results for Equations with Damping

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
M. Bartušek ◽  
John R. Graef
Keyword(s):  
Differential Equation ◽  
Limit Point ◽  
Second Order ◽  
Limit Circle

The authors study the nonlinear limit-point and limit-circle properties for the second order nonlinear damped differential equation(a(t)|y'|p-1y')'+b(t)|y'|q-1y'+r(t)|y|λ-1y=0, where0<λ≤p≤q,a(t)>0, andr(t)>0. Some examples are given to illustrate the main results.

Sign in / Sign up

Export Citation Format

Share Document