Related papers: On first and second order linear Stieltjes differe…

This work is devoted to the study of first order linear problems with involution and general linear conditions. We first study the problem in the case of antiperiodic boundary conditions, giving an explicit Green's function for it. Then we…

This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation…

This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…

We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and…

In this work we extend the theory of Stieltjes systems beyond the monotone case, establishing new chain rules, generalized versions of the Fundamental Theorem of Calculus, compactness tools for Peano-type results, and a $g$-exponential for…

We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0,…

Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…

We construct the Green function for second-order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that the Green's function is BMO in the domain and establish…

We give a new estimate on Stieltjes integrals of H\"older continuous functions and use it to prove an existence-uniqueness theorem for solutions of ordinary differential equations with H\"older continuous forcing. We construct stochastic…

We study the existence of Riemann-Stieltjes integrals of bounded functions against a given integrator. We are also concerned with the possibility of computing the resulting integrals by means of related Riemann integrals. In particular, we…

This work is devoted to the obtaining of a new numerical scheme based in quadrature formulas for the Lebesgue-Stieltjes integral for the approximation of Stieltjes ordinary differential equations. This novel method allows us to numerically…

We prove the existence and pointwise bounds of the Green functions for stationary Stokes systems with measurable coefficients in two dimensional domains. We also establish pointwise bounds of the derivatives of the Green functions under a…

We study various Stieltjes integrals as Poisson-Stieltjes, conjugate Poisson-Stieltjes, Schwartz-Stieltjes and Cauchy-Stieltjes and prove theorems on the existence of their finite angular limits a.e. in terms of the singular…

We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability…

In this paper we will show several properties of the Green's functions related to various boundary value problems of arbitrary even order. In particular, we will write the expression of the Green's functions related to the general…

We study existence and Lorentz regularity of distributional solutions to elliptic equations with either a convection or a drift first order term. The presence of such a term makes the problem not coercive. The main tools are pointwise…

In this paper we will deduce several properties of the Green's functions related to the Hill's equation coupled to various boundary value conditions. In particular, the idea is to study the Green's functions of the second order differential…

We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…

Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear…

In this paper we study some classes of second order non-homogeneous nonlinear differential equations allowing a specific representation for nonlinear Green's function. In particular, we show that if the nonlinear term possesses a special…