A Sign-changing Solution for a Superlinear Dirichlet Problem with a Reaction Term Nonzero at Zero

In previous joint work with A. Castro and J. Cossio (See 5]), it was shown that a superlinear boundary value problem has at least 3 nontrivial solutions, one of which changes sign exactly-once. In this paper we provide an analogous result when the nonlinearity does not pass through the origin; this case includes the so-called semiposi-tone case, i.e., where the nonlinearity is negative at zero. We nd a small negative solution and a pair of larger solutions (negative and and of nontrivial positive part respectively), together with a fourth solution which changes sign. We brieey mention a gradient descent algorithm which follows our method of proof and can be used to obtain approximations to the four solutions (See 14]).