On the method of upper and lower solutions in abstract cones
On the nonlocal Cauchy problem for semilinear fractional order evolution equations
In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first...
On the opial type criterion for the well-posedness of the Cauchy problem for linear systems of generalized ordinary differential equations
The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense , with a unique solution is considered....
On the question of generalized solution to algebro-differential systems.
On the solution of certain non-linear differential equations of the third order
On the solvability of singular BVPs for second-order ordinary differential equations
On the solvability of the weighted initial value problem for high-order evolution singular functional-differential equations.
On the stability analysis of Darboux problem on both bounded and unbounded domains
In this paper, we first investigate the existence and uniqueness of solution for the Darboux problem with modified argument on both bounded and unbounded domains. Then, we derive different types of the Ulam stability for the proposed problem on these domains. Finally, we present some illustrative examples to support our results.
On the stability of a fractional-order differential equation with nonlocal initial condition.
On the stability of some fractional-order non-autonomous systems.
On the Stability Properties of Brown's Multistep Multiderivative Methods.
On the terminal value problem for differential equations with deviating arguments
On the theorem of Filippov-Pliś and some applications
On the Timoshenko type equations
On Tykhonov's theorem for convergence of solutions of slow and fast systems.
On uniqueness of solutions of differential equations
One-sided conditions for quasilinear Jacobi differential equations
Optimal Control of a Cancer Cell Model with Delay
In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and existence...
Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension
We study some natural sets arising in the theory of ordinary differential equations in one variable from the point of view of descriptive set theory and in particular classify them within the Borel hierarchy. We prove that the set of Cauchy problems for ordinary differential equations which have a unique solution is -complete and that the set of Cauchy problems which locally have a unique solution is -complete. We prove that the set of Cauchy problems which have a global solution is -complete...
Ordinary differential equations the solution of which are -functions