Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at 0 and ∞ - Wenguo Shen (Discrete Dynamics in Nature and Society)
We study the existence of nodal solutions for the following problem: -x″=αx++βx-+ra(t)f(x), 0<t<1, x(0)=x(1)=0, where r≠0 is a parameter, a(t)∈C([0,1],(0,∞)) with a(t)≢0 on any subinterval of [0,1], x+=max{x,0},x-=-min{x,0}, and α,β∈C[0,1]; f∈C(R,R), sf(s)>0 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.