A method for finding the step size of integration of a system of ordinary differential equations
A method in diophantine approximation (VI)
A method of solving .
A method to solve an equation with left and right fractional derivatives
A model for gene activation.
A model of competition
A competition model is described by a nonlinear first-order differential equation (of Riccati type). Its solution is then used to construct a functional equation in two variables (admitting essentially the same solution) and several iterative functional equations; their continuous solutions are presented in various forms (closed form, power series, integral representation, asymptotic expansion, continued fraction). A constant C = 0.917... (inherent in the model) is shown to be a transcendental number....
A modification and comparison of Filippov and Viktorovskij generalized solutions
A modification of the Sturm's theorem on separating zeros of solutions of a linear differential equation of the 2nd order
A modified regularization method.
A modified version of explicit Runge-Kutta methods for energy-preserving
In this paper, Runge-Kutta methods are discussed for numerical solutions of conservative systems. For the energy of conservative systems being as close to the initial energy as possible, a modified version of explicit Runge-Kutta methods is presented. The order of the modified Runge-Kutta method is the same as the standard Runge-Kutta method, but it is superior in energy-preserving to the standard one. Comparing the modified Runge-Kutta method with the standard Runge-Kutta method, numerical experiments...
A monotone iterative method for boundary value problems of parametric differential equations.
A multiplicity result for periodic solutions to higher-order ordinary differential equations via the method of upper and lower solutions.
A necessary and sufficient condition for uniqueness of solutions of singular differential inequalities.
A new approach for solving nonlinear BVP's on the half-line for second order equations and applications
We present a new approach to solving boundary value problems on noncompact intervals for second order differential equations in case of nonlocal conditions. Then we apply it to some problems in which an initial condition, an asymptotic condition and a global condition is present. The abstract method is based on the solvability of two auxiliary boundary value problems on compact and on noncompact intervals, and uses some continuity arguments and analysis in the phase space. As shown in the applications,...
A new approach to inverse spectral theory. I: Fundamental formalism.
A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure.
A new approach to solve systems of second order non-linear ordinary differential equations.
A new approach to the existence results for orientor fields with Nicoletti's boundary conditions
Applying a global bifurcation theorem for convex-valued completely continuous mappings we prove some existence theorems for convex-valued differential inclusions of the form x'∈ F(t,x), where x satisfies the Nicoletti boundary conditions.
A new characteristic property of Mittag-Leffler functions and fractional cosine functions
A new characteristic property of the Mittag-Leffler function with 1 < α < 2 is deduced. Motivated by this property, a new notion, named α-order cosine function, is developed. It is proved that an α-order cosine function is associated with a solution operator of an α-order abstract Cauchy problem. Consequently, an α-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique α-order cosine function.
A new Green function concept for fourth-order differential equations.