Resonant problem for some second-order differential equation on the half-line

Abstract

We prove the existence of at least one solution to a nonlinear second-order differential equation on the half-line, with the boundary conditions $x'(0)=0$ and with the first derivative vanishing at infinity. Our main tool is the multi-valued version of the Miranda Theorem.

Keywords

• Asymptotic boundary value problem
• resonant problem
• nonlinear boundary value problem
• set-valued maps