Related papers: On the well posed solutions for nonlinear second o…
This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We provide a short proof, not utilizing complex numbers, for the solution set of homogeneous second order linear differential equations with constant coefficients.
We present an existence and localization result for periodic solutions of second-order non-linear coupled planar systems, without requiring periodicity for the non-linearities. The arguments for the existence tool are based on a variation…
Uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic type is established in one and two dimensions. In each case, we prove a comparison theorem based on locally bounding the variation of the discrete…
We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.
The problem of algebraic dependence of solutions to (non-linear) first order autonomous equations over an algebraically closed field of characteristic zero is given a `complete' answer, obtained independently of model theoretic results on…
It is well known that, under standard assumptions, initial value problems for fractional ordinary differential equations involving Caputo-type derivatives are well posed in the sense that a unique solution exists and that this solution…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
We establish a coupled fixed points theorem for a meaningful class of mixed monotone multivalued operators and then we use it to derive some results on existence of quasisolutions and solutions to first--order functional differential…
This note considers fairly general quasi-homogeneous systems of first-order nonlinear ODEs and homogeneous systems of second-order nonlinear ODEs that contain arbitrary functions of several arguments. It presents several exact solutions to…
For equations with the neutral term strictly delayed we construct the fundamental solution, derive a variation-of-constants formula for inhomogeneous equations, and prove growth estimates. Only unavoidable measure and integration theory, up…
A monotone iterative method is proposed to solve nonlinear discrete boundary value problems with the support of upper and lower solutions. We establish some new existence results. Under some sufficient conditions, we establish maximum…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
The purpose of this paper is to establish Picard-Lindel\"{o}f theorem for local uniqueness and existence results for first-order systems of nonlinear delay dynamic equations. In the linear case, we extend our results to global existence and…
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
This paper is devoted to the existence of positive solutions for a problem related to a fourth-order differential equation involving a nonlinear term depending on a second order differential operator, $$(-\Delta)^2 u=\lambda u+…
We study solutions $(x_n)_{n \in \mathbb{N}}$ of nonhomogeneous nonlinear second order difference equations of the type $\ell_n = x_n ( \sigma_{n,1} x_{n+1} + \sigma_{n,0} x_n + \sigma_{n,-1} x_{n-1} ) + \kappa_n x_n$, with given initial…
For a nonlinear ordinary differential equation with time delay, the differentiation of the solution with respect to the delay is investigated. Special emphasis is laid on the second-order derivative. The results are applied to an associated…
We investigate the existence of strong solutions to a general class of doubly multivalued and nonlinear evolution equations of second order. The multivalued operators are generated by the subdifferential of nonsmooth potentials that live in…