A family of singular ordinary differential equations of the third order with an integral boundary condition

Abstract

We establish in this paper the equivalence between a Volterra integral equation of the second kind and a singular ordinary differential equation of the third order with two initial conditions and an integral boundary condition, with a real parameter. This equivalence allows us to obtain the solution to some problems for non-classical heat equation, the continuous dependence of the solution with respect to the parameter and the corresponding explicit solution to the considered problem.

Existence theory for a third-order ordinary differential (equation, inclusion) with non-separated multi-point and nonlocal Stieltjes boundary conditions

“…Also can construct boundary value problems that contain random shapes such as fluid flow problems in the blood vessels. For the latest developments in the boundary value problems and their conditions we advise the researchers to look at the works [1]- [22].…”

Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions

“…On the other hand, integral boundary conditions play a key role in formulating the real world problems involving arbitrary shaped structures, for example, blood vessels in fluid flow problems [11][12][13]. For the recent development of the boundary value problems involving integral and multi-strip conditions, we refer the reader to the works [14][15][16][17][18][19].…”

Some new nonlinear second-order boundary value problems on an arbitrary domain

“…Integral boundary conditions find useful applications in blood flow problems [21,22], thermal conduction, semiconductor, and hydrodynamic problems [23][24][25]. One can find some works on boundary value problems involving integral boundary conditions in a series of papers [26][27][28][29][30][31][32][33] and the references cited therein.…”