New Oscillation Results of Second-Order Damped Dynamic Equations withp-Laplacian on Time Scales

By employing a generalized Riccati technique and functions in some function classes for integral averaging, we derive new oscillation criteria of second-order damped dynamic equation withp-Laplacian on time scales of the form(rtφγ(xΔ(t)))Δ+ptφγ(xΔ(t))+f(t,x(g(t)))=0, where the coefficient functionp(t)may change sign. Two examples are given to demonstrate the obtained results.

Interval Oscillation Criteria for Second-Order Forced Functional Dynamic Equations on Time Scales

This paper is concerned with oscillation of second-order forced functional dynamic equations of the form(r(t)(xΔ(t))γ)Δ+∑i=0n‍qi(t)|x(δi(t))|αisgn x(δi(t))=e(t)on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria.

Oscillation Criteria of Second-Order Dynamic Equations with Damping on Time Scales

Using functions in some function classes and a generalized Riccati technique, we establish Kamenev-type oscillation criteria for second-order dynamic equations with damping on time scales of the form(r(t)(xΔ(t))γ)Δ+p(t)(xΔ(t)γ)+f(t,x(g(t)))=0. Two examples are included to show the significance of the results.

Set of Oscillation Criteria for Second Order Nonlinear Forced Differential Equations with Damping

By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second order nonlinear forced differential equation with damping. These results extend, improve, and unify some known oscillation criteria in the existing literature.

Kamenev-Type Oscillation Criteria of Second-Order Nonlinear Dynamic Equations on Time Scales

Using functions from some function classes and a generalized Riccati technique, we establish Kamenev-type oscillation criteria for second-order nonlinear dynamic equations on time scales of the form(p(t)ψ(x(t))k∘xΔ(t))Δ+f(t,x(σ(t)))=0. Two examples are included to show the significance of the results.

Oscillation Criteria for Second-Order Nonlinear Dynamic Equations on Time Scales

This paper is concerned with oscillation of second-order nonlinear dynamic equations of the form on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria.

Interval Oscillation Criteria of Second-Order Nonlinear Dynamic Equations on Time Scales

Using functions in some function classes and a generalized Riccati technique, we establish interval oscillation criteria for second-order nonlinear dynamic equations on time scales of the form(p(t)ψ(x(t))xΔ(t))Δ+f(t,x(σ(t)))=0. The obtained interval oscillation criteria can be applied to equations with a forcing term. An example is included to show the significance of the results.

Oscillation Properties for Second-Order Partial Differential Equations with Damping and Functional Arguments

Using an integral averaging method and generalized Riccati technique, by introducing a parameterβ≥1, we derive new oscillation criteria for second-order partial differential equations with damping. The results are of high degree of generality and sharper than most known ones.

Oscillation Criteria Based on a New Weighted Function for Linear Matrix Hamiltonian Systems

By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second-order matrix differential systemU′=A(x)U+B(t)V,V′=C(x)U−A∗(t)V, whereA(t),B(t), andC(t)are(n×n)-matrices, andB,Care Hermitian. These results are sharper than some previous results.