Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞

Abstract

We study the existence of nodal solutions for the following problem: -x″=αx++βx-+ra(t)f(x), 00 for s≠0, and f0,f∞∉(0,∞), where f0=lim|s|→0f(s)/s and f∞=lim|s|→+∞f(s)/s. We use bifurcation techniques to prove our main results.