Multiplicity results for a class of superlinear elliptic problems

Abstract

We study a class of superlinear elliptic problems -Δu = λf(u) under the Dirichlet boundary condition on a bounded smooth domain in ℝ N . Assuming that the nonlinearity f(u) is superlinear in a neighborhood of u = 0, we study the dependence of the number of signed and sign-changing solutions on the parameter λ. © 2004 American Mathematical Society.