This paper studies the existence of symmetric positive solutions for a second-order nonlinear ordinary differential equation with integral boundary conditions by applying the theory of fixed point index in cones. For the demonstration of the results, an illustrative example is presented.
A computer-assisted proof of the existence of solutions to a boundary value problem with an integral boundary condition
โ Scribed by Oswald Fogelklou; Warwick Tucker; Gunilla Kreiss; Malin Siklosi
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 423 KB
- Volume
- 16
- Category
- Article
- ISSN
- 1007-5704
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โฆ Synopsis
In this paper, we present a computer-assisted method that establishes the existence and local uniqueness of a stationary solution to the viscous Burgers' equation. The problem formulation involves a left boundary condition and one integral boundary condition, which is a variation of a previous approach.
๐ SIMILAR VOLUMES
This paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary-value problems of fourth-order differential equations with integral boundary conditions. The arguments are based upon a specially constructed cone and the fixed-point theory in cone. The no