Some investigations on a class of nonlinear integrodifferential equations on the half-line

Abstract

We consider the second-order integrodifferential boundary value problem

$$\left\{\begin{array}{c}\hfill \\ \hfill \\ \nu \left(y\right)g\left(y\right)-{\int }_0^{+\infty }k\left(x\right)g\left(x\right)dx@{\left[D\left(y\right)g^{\prime }\left(y\right)@\right]}^{@\prime }=p\left(y\right)\text{ for }y\ge 0,\hfill \\ \hfill \\ \hfill \\ g^{\prime }\left(0\right)=0,g\left(+\infty \right)=0,\hfill \\ \hfill \\ \hfill \\ \hfill \end{array}\right.$$

arising from the kinetic theory of dusty plasmas, and we provide information on the existence and other qualitative properties of the solution that have been essential in the numerical investigation.