The free boundary for a fourth order variational inequality

The variational iteration method for a class of tenth-order boundary value differential equations

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...

Variational Iteration Method for Free Vibration Analysis of a Timoshenko Beam under Various Boundary Conditions

In this paper, a relatively new method, namely variational iteration method (VIM), is developed for free vibration analysis of a Timoshenko beam with different boundary conditions. In the VIM, an appropriate Lagrange multiplier is first chosen according to order of the governing differential equation of the boundary value problem, and then an iteration process is used till the desired accuracy ...

A Pointwise Inequality for the Fourth Order Lane-emden Equation

We prove that the following pointwise inequality holds −∆u ≥ √ 2 (p + 1)− cn |x| a 2 u p+1 2 + 2 n− 4 |∇u|2 u in R where cn := 8 n(n−4) , for positive bounded solutions of the fourth order Hénon equation that is ∆u = |x|u in R where a ≥ 0 and p > 1. Motivated by the Moser iteration argument in the regularity theory, we develop an iteration argument to prove the above pointwise inequality. As fa...

Error estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality

— We study a free-boundary problem ofbiological interest, for the heat équation ; the problem is reduced to a variational inequality, which is solved by means ofafinite différence method. We aiso give an error estimaté, in the L^-norm, for the solution of the inequality, and a convergence theorem for the discrete free boundaries, The latter follows from a gênerai resuit concerning the behaviour...