The purpose of this work is to consider an initial value problem for neutral functional diierential equations with state dependent and vanishing delays. A gener-alised version of Schauder's xed point theorem which is based on the ball measure of noncompactness is used to obtain local existence of solutions and a comparison theorem. Results on continuation, uniqueness and continuous dependence o...

We provide cubature formulas for the calculation of derivatives of expected values in the spririt of Terry Lyons and Nicolas Victoir. In financial mathematics derivatives of option prices with respect to initial values, so called Greeks, are of particular importance as hedging parameters. The proof of existence of Cubature formulas for Greeks is based on an argument, which leads to the calculat...

‎This paper gives an abstract order-type existence theorem for second order nonlocal boundary value problems at resonance and obtain existence criteria for at least two positive solutions‎, ‎where $f$ is a continuous function‎. ‎Our results generalize or extend related results in the literature and give a positive answer to the question raised in the literature‎. ‎An example is given to illustr...

<p style='text-indent:20px;'>The present paper proposes, in a real separable Hilbert space, to analyze the existence of solutions for class perturbed second-order state-dependent maximal monotone operators with finite delay. The dependence is -in some sense- absolutely continuous (or bounded continuous) variation time, and Lipschitz state. approach solve our problem based on discretizatio...

We consider mixed problems for infinite systems of first order partial functional differential equations. Infinite number of deviating functions is permitted, and the delay of an argument may depend also on spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existenc...

The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is...