Sign-Changing Solutions and Multiple Solutions Theorems for Semilinear Elliptic Boundary Value Problems with a Reaction Term Nonzero at Zero

In this paper, we use the ordinary differential equation theory of Banach spaces and minimax theory, in particular, the local mountain pass lemma to study asymptotically linear and superlinear elliptic boundary value problems with a reaction term nonzero at zero, and get new multiple solutions and sign-changing solutions theorems. Moreover, the sign-changing solutions change sign exactly once under some conditions.