A one-dimensional Kirchhoff equation with generalized convolution coefficients
The author studies, by means of classical fixed point index theory, the existence of at least one positive solution of the generalized one-dimensional Kirchhoff-type equation of the form \[ - A((a* (u')^q)(1)) u''(t)=\lambda f(t, u(t))\,\text{for}\, t\in (0,1), \] where \(q\geq 1\), subject to the right-focal boundary conditions \[ u(0)=0,\quad u'(1)=0. \] The choice of the convolution term in the differential equation is very flexible and covers a variety of situations, including fractional derivative coefficients of Caputo type.
scientific article; zbMATH DE number 7433415
scientific article