Oscillation and asymptotic behavior for second-order nonlinear neutral dynamic equations on measure chains;

Oscillation Criteria For A Class of Delay Differential System on Measure Chains;

The theory of dynamic equations on measure chains,introduced by Stefan Hilger in 1988,unifies and extends continuous and discrete analysis and also provides a framework for studying general class of dynamic equations.

Multivalued solutions of eigenvalue problems of nonlinear differential equation on measure chain;

Eigenvalue problem for a nonlinear differential equation on a measure chain;

Existence of solution for fourth-order four-point boundary value problems on measure chain

Oscillation for second-order nonlinear delay dynamic equations on time scales;

Existence of a solution to three-point BVPs for p-Laplacian dynamic equations on time scales;

Existence of solutions for second-order dynamic inclusions with boundary value conditions on time scales

In this paper,by means of Riccati transformation technique,we establish oscillation criteria for second-order nonlinear dynamic equations on time scales(r(t)x△)△+p(t)xγ(σ(t))=0,where p is positive real value rd-continuous function defined on T,and is quotient of odd positive integers,such that γ≥1.

In this paper,by using Riccati transformation technique,we establish oscillation criteria for a class of nonlinear second-order delay dynamic equations on time scales x△△(t)+p(t)x△(t)+q(t)f(x(τ(t)))=0,where p and q are positive real value rd-continuous functions defined on T.

These results are new even for the corresponding differential (T=R)and difference equation(T=Z),as well as general time scales setting.