A Sufficient Disconjugacy Condition for the Third Order Differential Equation
A super-integrable two-dimensional nonlinear oscillator with an exactly solvable quantum analog.
A survey of partial differential equations with piecewise continuous arguments.
A survey of the spectral and differential geometric aspects of the generalized de Rham-Hodge theory related with Delsarte transmutation operators in multidimension and applications to spectral and soliton problems. I.
A survey of the spectral and differential geometric aspects of the generalized De Rham-Hodge theory related with Delsarte transmutation operators in multidimension and applications to spectral and soliton problems. II.
A survey on oscillation of impulsive ordinary differential equations.
A system of non-linear functional differential equations arising in an equilibrium model of an economy with borrowing constraints
A theorem about Carathéodory's superposition
A theory of linear differential equations with fractional derivatives
A unified approach to abstract linear nonautonomous parabolic equations
A Uniform Scheme for the Singularly Perturbed Riccati Equation.
A uniqueness result for ordinary differential equations with singular coefficients.
A useful proposition to nonlinear differential systems with a solution of the prescribed asymptotic properties
A variational approach to implicit ODEs and differential inclusions
An alternative approach for the analysis and the numerical approximation of ODEs, using a variational framework, is presented. It is based on the natural and elementary idea of minimizing the residual of the differential equation measured in a usual Lp norm. Typical existence results for Cauchy problems can thus be recovered, and finer sets of assumptions for existence are made explicit. We treat, in particular, the cases of an explicit ODE and a differential inclusion. This approach also allows...
A vector functional equation and linear differential equations.
A verified method for solving piecewise smooth initial value problems
In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview...
A viability result for nonconvex semilinear functional differential inclusions
We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.
A viability result for second-order differential inclusions.
A viability result in the upper semicontinuous case.
A view on differential inclusions.