Tadeusz Jankowski

Differential equations with integral boundary conditions

The method of lower and upper solutions combined with monotone iterative technique is used for ordinary differential equations with integral boundary conditions. Problems of existence of extremal and unique solutions are discussed. Some comparison results are formulated too.

Differential Inequalities with Initial Time Difference

Some comparison results are obtained for differential inequalities with initial time difference. They are useful to get existence and stability theorems for differential equations.

Integro-differential inequalities with initial time difference and applications

Integro-differential inequalities with initial time difference arediscussed. They play an important role in the investigation of initial value problems of integro-differential equations where the initial time differs. The existence of extremal solutions is investigated by the monotone iterative technique.

Boundary value problems for ODEs

We use the method of quasilinearization to boundary value problems of ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic.

Monotone Iterations for First Order Differential Equations with a Parameter

The method of lower and upper solutions is useful to show that a differential problem has a solution. In this paper we use this technique to a differential problem with a parameter. Some existence results are formulated under the assumption that the corresponding functions satisfy the one-sided Lipschitz condition.

Antiperiodic Boundary Value Problems for Functional Differential Equations

In this paper, the method of quasilinearization has been extended to antiperiodic boundary value problems of nonlinear functional differential equations. It is shown that iterations converge to the unique solution and this convergence is semi-superlinear.

Second order differential equations with Dirichlet boundary conditions

In this paper we use a quasilinearization method to find an approximate solution of a nonlinear Dirichlet problem for second order differential equations. Sufficient conditions are formulated to obtain weak-quadratic, semi-quadratic or quadratic convergence of approximate solutions.

Numerical-Analytic Methods for Differential-Algebraic Systems

The numerical-analytic method is useful to show that a differential equation with a boundary condition has a solution. In this paper we use this method to differential-algebraic systems with boundary conditions. Some existence results are formulated under assumptions that the corresponding functions satisfy Lipschitz conditions in matrix notation.

Existence and approximate solutions of Neumann problems

A generalized quasilinearization technique is applied to a Neumann problem constructing sequences of approximate solutions converging to a solution. This convergence may be quadratic, semi-quadratic or weakly quadratic.

Samoilenko's method to differential algebraic systems with integral boundary conditions

The numerical analytic method combined with the comparison one is used to establish solvability of differential algebraic systems with integral boundary conditions. Existence results are formulated under assumptions that corresponding functions satisfy the Lipschitz conditions in matrix notation. A problem with deviated arguments is also discussed.