Multiple positive symmetric solutions to -Laplacian dynamic equations on time scales.
Necessary and sufficient conditions for stability of Volterra integro-dynamic equation on time scales
In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.
Necessary and sufficient conditions for the existence of positive solution for singular boundary value problems on time scales.
New fixed point theorems of mixed monotone operators and applications to singular boundary value problems on time scales.
Nonlinear scalar two-point boundary-value problems on time scales.
Nonoscillation Criteria for Two-Dimensional Time-Scale Systems
We study the existence and nonexistence of nonoscillatory solutions of a two-dimensional systemof first-order dynamic equations on time scales. Our approach is based on the Knaster and Schauder fixed point theorems and some certain integral conditions. Examples are given to illustrate some of our main results.
Nonoscillation of first-order dynamic equations with several delays.
Nonoscillation of second-order dynamic equations with several delays.
Nonoscillatory solutions for higher-order neutral dynamic equations on time scales.
Normal and osculating planes of -regular curves.
On a nonstandard Volterra type dynamic integral equation on time scales.
On the existence of solutions for dynamic boundary value problems under barrier strips condition.
On the existence of solutions for impulsive Duffing dynamic equations on time scales with Dirichlet boundary conditions.
On the oscillation of second-order neutral delay differential equations.
Opial's type inequalities on time scales and some applications
We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential...
Oscillation and nonoscillation criteria for two-dimensional time-scale systems of first-order nonlinear dynamic equations.
Oscillation behavior of a class of second-order dynamic equations with damping on time scales.
Oscillation behavior of third-order neutral Emden-Fowler delay dynamic equations on time scales.
Oscillation criteria for a class of second-order neutral delay dynamic equations of Emden-Fowler type.
Oscillation criteria for second order impulsive dynamic equations on time scales.