Existence of positive solutions of superlinear second-order Neumann boundary value problem

In this paper, we consider the Neumann boundary value problem {−(p(t)u′(t))′+q(t)u(t)=f(t,u(t)),t∈(0,1)u′(0)=u′(1)=0, where p∈C1[0,1],p(t)>0p∈C1[0,1],p(t)>0, q∈C[0,1],q(t)≥0q∈C[0,1],q(t)≥0, f∈C([0,1]×(−∞,+∞),(−∞,+∞))f∈C([0,1]×(−∞,+∞),(−∞,+∞)). By using topological degree theory, we investigate the existence of nontrivial solutions. In particular, we prove the existence of positive solutions provided that q(t)>0q(t)>0.