Bifurcation from infinity for an asymptotically linear problem on the half-line

This paper is concerned with asymptotic bifurcation for a semilinear equation on the half-line. For an asymptotically linear nonlinearity, the existence of a continuum of solutions ‘bifurcating from infinity’ is obtained by using a topological degree. Under additional monotonicity conditions, the continuum is shown to be a continuous curve. Applications to nonlinear planar waveguides are mentioned.