ON THE LIMIT-POINT, LIMIT-CIRCLE CLASSIFICATION OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS

1973 ◽  
Vol 24 (1) ◽  
pp. 531-535 ◽  
Author(s):  
M. S. P. EASTHAM ◽  
M. L. THOMPSON
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Limit Point ◽  
Second Order ◽  
Limit Circle

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.

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.

22.—A Critical Class of Examples concerning the Integrable-square Classification of Ordinary Differential Equations

1976 ◽  
Vol 74 ◽  
pp. 285-297 ◽  
Author(s):  
W. N. Everitt ◽  
M. Giertz
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Limit Point ◽  
Half Line ◽  
Absolutely Continuous ◽  
Negative Numbers ◽  
Independent Variable ◽  
Image Position ◽  
Critical Class

SynopsisLet the coefficient q be real-valued on the half-line [0, ∞) and let q′ be locally absolutely continuous on [0, ∞). The ordinary symmetric differential expressions M and M2 are determined byIt has been shown in a previous paper by the authors that if for non-negative numbers k and X the coefficient q satisfies the conditionthen M is limit-point and M2 is limit–2 at ∞.This paper is concerned with showing that for powers of the independent variable x the condition (*) is best possible in order that both M and M2 should have the classification at ∞ given above.

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