The Dirichlet Problem for an Ordinary Continuous Second-Order Differential Equation
- 12 Downloads
The extremum principle for an ordinary continuous second-order differential equation with variable coefficients is proved and this principle is used to establish the uniqueness of the solution of the Dirichlet problem. The problem under consideration is equivalently reduced to the Fredholm integral equation of the second kind and the unique solvability of this integral equation is proved.
Keywordscontinuous differential equation fractional integro-differential operator Dirichlet problem extremum principle
Unable to display preview. Download preview PDF.
- 2.A. M. Nakhushev, “On the positivity of continuous and discrete differentiation and integration operators that are very important in fractional calculus and in the theory of equations of mixed type,” Differ. Uravn. 34 (1), 101–109 (1998) [Differ. Equations 34 (1), 103–112 (1998)].MathSciNetGoogle Scholar
- 10.B. I. Éfendiev, “Steklov problemfor a second-order ordinary differential equation with a continual derivative,” Differ. Uravn. 49 (4), 469–475 (2013) [Differ. Equations 49 (4), 450–456 (2013)].Google Scholar