Existence of optimal boundary control for the Navier–Stokes equations with mixed boundary conditions

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Optimal control of stochastic differential equations with dynamical boundary conditions

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problem with non standard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. In other terms, we are concerned with non standard boundary conditi...

The existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions

In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,...

Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions

and Applied Analysis 3 Definition 2.1. The fractional arbitrary order integral of the function h ∈ L1 J, R of order α ∈ R is defined by I 0h t 1 Γ α ∫ t 0 t − s α−1h s ds, 2.1 where Γ · is the Euler gamma function. Definition 2.2. For a function h given on the interval J , Caputo fractional derivative of order α > 0 is defined by D α 0 h t 1 Γ n − α ∫ t 0 t − s n−α−1h n s ds, n α 1, 2.2 where t...

Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions