This work presents the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (nth-CASAM-N), which enables most efficient computation of exactly determined expressions arbitrarily high-order sensitivities generic nonlinear system responses with respect to model parameters, uncertain boundaries, and internal interfaces in model’s phase space. The mathematical fram...

where n >, 2, a: [0, 00) + [0, a~), q: [0, co) --+ (-00, co), andf: (--co, 03) + (-00, CQ). We assume a(l), q(t), andf( x are continuous, q(t) < t for all t > 0, q(t) 3 co ) as t ---f co, and xf(x) > 0 for x # 0. Usually, a condition of monotonicity on f is needed in order to obtain results for Eq. (1) analogous to those of an ordinary differential equation of the same type. Many authors observ...

Sufficient conditions are given under which the nonlinear n-th order differential equation with quasiderivatives has oscillatory solutions. AMS Subject Classification. 34C10

and Applied Analysis 3 Now one rewrites 1.1 as the following equivalent system ( x t px t − 1 )′ y1 t , 2.31 y′ 1 t y2 t , 2.32 .. .. y′ N−2 t yN−1 t , 2.3N−1 y′ N−1 t qx t f t . 2.3N 2.3 Let x t , y1 t , . . . , yN−1 t be solutions of system 2.3 on , for n ≤ t < n 1, n ∈ , using 2.3N we obtain yN−1 t yN−1 n qx n t − n ∫ t

Shooting methods are employed to obtain solutions of multipoint boundary value problem for the nth order equation, y = f(x, y, y′, . . . , y(n−1)), satisfying boundary conditions for which solutions are unique, under a right disfocality assumption.

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

and Applied Analysis 3 Now, let f̃ : R 1 → R be a continuous function, T -periodic with respect to the first variable, and consider the nth-order differential equation u n f̃ ( t, u, u′, u′′, . . . , u n−1 ) . 2.5 Lemma 2.1 see 14 . Assume that the following conditions hold. i There exists ρ > 0 such that, for each λ ∈ 0, 1 , one has that any possible T -periodic solution u of the problem u n λf̃ ...

We prove existence results for solutions of periodic boundary value problems concerning the nth-order differential equation with p-Laplacian [φ(x(n−1)(t))]′ = f (t,x(t),x′(t), . . . , x(n−1)(t)) and the boundary value conditions x(i)(0)=x(i)(T), i= 0, . . . ,n− 1. Our method is based upon the coincidence degree theory of Mawhin. It is interesting that f may be a polynomial and the degree of som...

where 01, ,l3, y and the x’s are real. It will be assumed throughout this paper that f (t, Ul , u, ,.-., un) is continuous on [CX, r] x R”. The approach taken here is similar to that of Barr and Sherman [I] and is based on the use of a solutionmatching technique that assumes existence and/or uniqueness of solutions to corresponding problems for the subintervals [cu, ,Kj and [p, y]. We refer to ...

Abstract: In order that the nth-order Generalized Frequency Response Function (GFRF) for nonlinear systems described by a NARX model can be directly written into a more straightforward and meaningful form in terms of the first order GFRF and model parameters, the nth-order GFRF is now determined by a new mapping function based on a parametric characteristic. This can explicitly unveil the linea...