Three positive solutions to an indefinite Neumann problem: A shooting method

We deal with the Neumann boundary value problem u′′+(λa+(t)−μa−(t))g(u)=0,0<1,∀t∈[0,T],u′(0)=u′(T)=0,where the weight term has two positive humps separated by a negative one and g:[0,1]→R is a continuous function such that g(0)=g(1)=0, g(s)>0 for 0<1 and lims→0javax.xml.bind.JAXBElement@501dbb92g(s)∕s=0. We prove the existence of three solutions when λ and μ are positive and sufficiently large.