In this paper, using the hyperbolic uniform spline of order 4 we develop the classes of methods for the numerical solution of second order boundary value problems (2VBP) with Dirichlet, Neumann and Cauchy types boundary conditions. The second derivativeis approximated by the three-point central difference scheme. The approximate results, obtained by the proposed method, confirm theconvergence o...

We study the existence and multiplicity of positive solutions of the following boundary-value problem: −u 6 − γu 4 βu − αu ft, u, 0 < t < 1, u0 u1 u 0 u 1 u 4 0 u 4 1 0, where f : 0, 1× R → R is continuous, α, β, and γ ∈ R satisfy some suitable assumptions.

In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...

krein [1] mentioned that for each pd equation we have two extreme operators, one is the minimal in which solution and its derivatives on the boundary are zero, the other one is the maximal operator in which there is no prescribed boundary conditions. they claim it is not possible to have a related boundary value problem for an arbitrarily chosen operator in between. they have only considered lo...

where A(t), B(t), C(t) Î C[0,1], f(t, u) : [0,1] × [0, ∞) ® [0. ∞) is continuous. In recent years, BVPs for sixth-order ordinary differential equations have been studied extensively, see [1-7] and the references therein. For example, Tersian and Chaparova [1] have studied the existence of positive solutions for the following systems (1.2): { u(6) + Au(4) + Bu′′ + Cu − f (t, u) = 0. 0 < x < L, u...