Bifurcation from infinity in nonlinear sturm liouville problems with different linearizations at ‘u = ±∞’

Abstract

We consider large solutions of the nonlinear Sturm Liouville problem

, Where a_i,b_i are real numbers with |a_i|+|b_i| > 0, i = 0, 1. The existence of global continua of solutions (λ, u), with large u, bifurcating from infinity has been discussed by Rabinowitz and Toland when the problem is ;asymptotically linear for large u. In this paper we will obtain similar results when the problem has different asymptotic linearizations at u = ±∞ (and hence is not asymptotically linear, so the preceding results do not apply).

Keywords:

• Bifurcation from infinity
• nonlinear Sturm Liouville problems