Bifurcation and nodal solutions for pp-Laplacian problems with non-asymptotic nonlinearity at 0 or ∞∞

In this work, we study the existence of nodal solutions for the following problem: {(φp(u′))′+λa(t)f(u)=0,t∈(0,1),u(0)=u(1)=0, where φp(s)=|s|p−2sφp(s)=|s|p−2s, a∈C([0,1],[0,+∞))a∈C([0,1],[0,+∞)) with a≢0a≢0 on any subinterval of [0,1][0,1] and f:R→Rf:R→R is continuous with f(s)s>0f(s)s>0 for s≠0s≠0. We give the intervals for the parameter λλ which ensure the existence of single or multiple nodal solutions for the problem if f0∉(0,+∞)f0∉(0,+∞) or f∞∉(0,+∞)f∞∉(0,+∞), where f(s)/φp(s)f(s)/φp(s) approaches f0f0 and f∞f∞ as ss approaches 00 and ∞∞, respectively. We use bifurcation techniques to prove our main results.