Navier–Stokes Equations with First Order Boundary Conditions

boundary layer problem for system of first order of ordinary differential equations with linear non-local boundary conditions

in this paper we study the boundary layer problems in which boundary conditions are non-local. here we try to find the necessary conditions by the help of fundamental solution to the given adjoint equation. by getting help from these conditions, at first the boundary condition is changed from non-local to local. the main aim of this paper is to identify the location of the boundary layer. in ot...

Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary conditions

In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on whi...

Existence Theorem for First Order Ordinary Functional Differential Equations with Periodic Boundary Conditions

Nonlinear boundary value problems for first order integro-differential equations with impulsive integral conditions∗

This paper is concerned with the nonlinear boundary value problems for first order integro-differential equations with impulsive integral conditions. By using of the method of lower and upper solutions coupled with the monotone iterative technique, we give conditions for the existence of extremal solutions.

Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions

We present an existence theorem for nonlinear ordinary differential equations of first order with nonlinear boundary conditions. The result includes, for instance, the initial value problem, the final value problem, and the antiperiodic boundary value problem. The main novelty of the method lies in that it unifies different techniques for initial or boundary conditions.