We apply the generalized quasilinearization technique to obtain a monotone sequence of iterates converging quadratically to the unique solution of a general second order nonlinear differential equation with nonlinear nonlocal mixed three-point boundary conditions. The convergence of order n (n ≥ 2) of the sequence of iterates has also been established.

*Correspondence: [email protected] Department of Mathematics, Shaoxing University, Shaoxing, Zhejiang 312000, P.R. China Abstract This paper is concerned with fractional differential inclusions with three-point fractional integral boundary conditions. We consider the fractional differential inclusions under both convexity and nonconvexity conditions on the multivalued term. Some new existenc...

The differentiation matrix for a Daubechies-based wavelet basis defined on an interval will be constructed. It will be shown that the differentiation matrix based on the currently available boundary constructions does not maintain the superconvergence encountered under periodic boundary conditions. BJgy .. .. . .. .A0000 w__ •t!ar ~'..,-

We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0, 2π). The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove th...

The paper is concerned with linear thermoelastic plate equations in a domain Ω: utt +∆u+∆θ = 0 and θt −∆θ −∆ut = 0 in Ω× (0,∞), subject to Dirichlet boundary condition: u|Γ = Dνu|Γ = θ|Γ = 0 and initial condition: (u, ut, θ)|t=0 = (u0, v0, θ0) ∈W 2 p,D(Ω)×Lp×Lp. Here, Ω is a bounded or exterior domain in R (n ≥ 2). We assume that the boundary Γ of Ω is a C hypersurface and we define W 2 p,D by ...

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinear qdifference equations with three-point q-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach’s contraction mapping, Krasnoselskii’s fixed-point theorem, and Leray-Schauder degree theory, some ...

This paper studies a coupled system of nonlinear fractional differential equation with three-point boundary conditions. Applying the Schauder fixed point theorem, an existence result is proved for the following system Du (t) = f (t, v (t) , Dv (t)) , t ∈ (0, 1) , Dv (t) = g (t, u (t) , Du (t)) , t ∈ (0, 1) , u (0) = 0, Du (1) = δDu (η) , v (0) = 0, Dv (1) = δDv (η) , where α, β, m, n, η, δ, θ s...

The notion of "mixtures" has become pervasive in behavioral and cognitive sciences, due to the success of dual-process theories of cognition. However, providing support for such dual-process theories is not trivial, as it crucially requires properties in the data that are specific to mixture of cognitive processes. In theory, one such property could be the fixed-point property of binary mixture...

In this paper we consider the problem of estimating the state, and identifying parameters of a diffusion process, when the only available information is the crossing times of a boundary. By using a partial differential equation approach related with the computation of boundary–crossing probabilities, we derive finite dimensional reconstructors (filters) for the state and Feynman Kac type functi...