scholarly journals Extensions of symmetric singular second-order dynamic operators on time scales

Filomat ◽  
2016 ◽  
Vol 30 (6) ◽  
pp. 1475-1484 ◽  
Author(s):  
Bilender Allakhverdiev
Keyword(s):  
Boundary Conditions ◽  
Time Scales ◽  
Limit Point ◽  
Second Order ◽  
Boundary Values ◽  
Infinite Time ◽  
Limit Circle ◽  
Symmetric Operators

A space of boundary values is constructed for minimal symmetric singular second-order dynamic operators on semi-infinite and infinite time scales in limit-point and limit-circle cases. A description of all maximal dissipative, maximal accumulative, selfadjoint, and other extensions of such symmetric operators is given in terms of boundary conditions.

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-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.

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 J-Self-Adjoint Extensions for a Class of Discrete Linear Hamiltonian Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-19
Author(s):  
Guojing Ren ◽  
Huaqing Sun
Keyword(s):  
Boundary Conditions ◽  
Hamiltonian Systems ◽  
Limit Point ◽  
Limit Circle ◽  
Linear Hamiltonian Systems ◽  
Infinite Intervals ◽  
Defect Indices

This paper is concerned with formallyJ-self-adjoint discrete linear Hamiltonian systems on finite or infinite intervals. The minimal and maximal subspaces are characterized, and the defect indices of the minimal subspaces are discussed. All theJ-self-adjoint subspace extensions of the minimal subspace are completely characterized in terms of the square summable solutions and boundary conditions. As a consequence, characterizations of all theJ-self-adjoint subspace extensions are given in the limit point and limit circle cases.

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