Carathéodory's method for a class of second order differential equations on the half-line
The authors study the following boundary value problem \[ (p(t)x'(t))'-f(t,x(t))=0,\;\;t\in(0,+\infty), \] \[ x(0)=\alpha,\;\;x(+\infty)=\beta, \] where \(p:(0,+\infty)\to (0,+\infty)\) is a continuously differentiable function, \(f:(0,+\infty)\times \mathbb R\to \mathbb R\) is a continuous function and \(\alpha\), \(\beta\) are given real constants. By extending the classical Carathéodory method for free problems in the calculus of variations they provide a~technique for obtaining the solutions to differential equations on the half-line.
scientific article; zbMATH DE number 5078891