Computation of Green's matrices for boundary value problems associated with a pair of mixed linear regular ordinary differential operators.
Computation of topological degree in ordered Banach spaces with lattice structure and applications
Using the cone theory and the lattice structure, we establish some methods of computation of the topological degree for the nonlinear operators which are not assumed to be cone mappings. As applications, existence results of nontrivial solutions for singular Sturm-Liouville problems are given. The nonlinearity in the equations can take negative values and may be unbounded from below.
Computationally efficient technique for solving ODE systems exhibiting initial and boundary layers.
Computing eigenvalues of regular Sturm-Liouville problems.
Concave Solutions of Singular Non-linear Differential Equations.
Conditional differential equations
We introduce and study conditional differential equations, a kind of random differential equations. We give necessary and sufficient conditions for the existence of a solution of such an equation. We apply our main result to a Malthus type model.
Conditioning of three-point boundary value problems associated with first order matrix Lyapunov systems.
Conditions for existence and uniqueness of solutions to multipoint boundary value problems for systems of generalized ordinary differential equations.
Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas....
Construction of non-constant lower and upper functions for impulsive periodic problems.
Construction of upper and lower solutions for singular discrete initial and boundary value problems via inequality theory.
Constructions of lower and upper solutions for a nonlinear boundary value problem of the third order and their applications
Continuous dependence and differentiation of solutions of finite difference equations.
Continuous dependence on data for quasiautonomous nonlinear boundary value problems.
Continuous dependence on parameters for second order discrete BVP’s
Using Fan’s Min-Max Theorem we investigate existence of solutions and their dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle points to the relevant Euler action functional.
Continuous solutions of nonlinear boundary value problems for ODE's on unbounded intervals
Contribution a la théorie des équations non linéaires dans les espaces de Banach [Book]
Convergence acceleration of shifted transformations for totally nonnegative Hessenberg matrices
We design shifted transformations based on the integrable discrete hungry Toda equation to compute eigenvalues of totally nonnegative matrices of the banded Hessenberg form. The shifted transformation can be regarded as an extension of the extension employed in the well-known dqds algorithm for the symmetric tridiagonal eigenvalue problem. In this paper, we propose a new and effective shift strategy for the sequence of shifted transformations by considering the concept of the Newton shift....
Convergence of a mimetic finite difference method for static diffusion equation.
Convergence of eigenfunction expansions corresponding to nonlinear Sturm-Liouville operators.