Even order self adjoint time scale problems.
Eventually periodic solutions for difference equations with periodic coefficients and nonlinear control functions.
Exact asymptotics of nonlinear difference equations with levels and
We study a class of nonlinear difference equations admitting a -Gevrey formal power series solution which, in general, is not - (or Borel-) summable. Using right inverses of an associated difference operator on Banach spaces of so-called quasi-functions, we prove that this formal solution can be lifted to an analytic solution in a suitable domain of the complex plane and show that this analytic solution is an accelero-sum of the formal power series.
Exact stability regions for linear difference equations with three parameters.
Exact traveling wave solutions for discrete conservation laws.
Existence and global attractivity of periodic solutions in a higher order difference equation
Consider the following higher order difference equation where and are continuous functions in and periodic functions in with period , and is a nonnegative integer. We show the existence of a periodic solution under certain conditions, and then establish a sufficient condition for to be a global attractor of all nonnegative solutions of the equation. Applications to Riccati difference equation and some other difference equations derived from mathematical biology are also given.
Existence and global attractivity positive periodic solutions for a discrete model.
Existence and global stability of positive periodic solutions of a discrete predator-prey system with delays.
Existence and global stability of positive periodic solutions of a discrete delay competition system.
Existence and multiple solutions for nonlinear second-order discrete problems with minimum and maximum.
Existence and multiplicity of solutions for discrete nonlinear two-point boundary value problems.
Existence and multiplicity of solutions to discrete conjugate boundary value problems.
Existence and nonexistence of positive solutions to a right-focal boundary value problem on time scales.
Existence and positivity of solutions for a nonlinear periodic differential equation
We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.
Existence and uniqueness of nontrivial solutions for nonlinear higher-order three-point eigenvalue problems on time scales.
Existence and uniqueness of positive solution for singular BVPs on time scales.
Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations.
Existence criteria and classification schemes for positive solutions of second-order nonlinear difference systems.
Existence criteria for positive solutions of a nonlinear difference inequality
This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.
Existence for a class of discrete hyperbolic problems.