Differential Equations of Order Two with One Singular Point

On Two-point Boundary Value Problems for Higher Order Singular Ordinary Differential Equations

is integrable in the first argument on [a + ε, b − ε] for arbitrary ρ ∈ [0,+∞[ and ε ∈ ]0, (b− a)/2[ . Of special interest for us is the case where the function f (and therefore the function f) is non-integrable in the first argument on [a, b], having singularities at the ends of this segment. In this sense the problems (1), (2) and (1), (3) are singular ones. Singular boundary value problems f...

First-Order Singular and Discontinuous Differential Equations

Two–point Oscillations in Second–order Linear Differential Equations

A second-order linear differential equation (P) : y′′ + f (x)y = 0 , x ∈ I , where I = (0,1) and f ∈ C(I) , is said to be two-point oscillatory on I , if all its nontrivial solutions y ∈ C( I )∩C2(I) , oscillate both at x = 0 and x = 1 , i.e. having sequences of infinite zeros converging to x = 0 and x = 1 . It necessarily implies that all solutions y(x) of (P) must satisfy the Dirichlet bounda...

Fuzzy laplace transform on two order derivative and solving fuzzy two order differential equations

INVESTIGATION OF BOUNDARY LAYERS IN A SINGULAR PERTURBATION PROBLEM INCLUDING A 4TH ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we investigate a singular perturbation problem including a fourth order O.D.E. with general linear boundary conditions. Firstly, we obtain the necessary conditions of solution of O.D.E. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.