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 prim...

We consider the steady state Stokes equations, describing low speed ow and derive estimates of the solution for various types of boundary conditions. We formulate the boundary conditions in a new way, such that the boundary value problem becomes non-singular. By using a di erence approximation on a staggered grid we are able to derive a non-singular approximation in a direct way. Furthermore, w...

Abstract. We consider solutions of the equation −Δu + λu + |∇u|q = f , which blow up uniformly at the boundary of a smooth domain, that can be interpreted as the value function of a state constraint control problem for a Brownian motion. We prove a complete asymptotic expansion of the gradient at the boundary, giving the precise behavior of normal and tangent components. The result is achieved ...