Multiple solutions with sign information for Robin equations with indefinite potential

Abstract

In this paper, we study a Robin boundary value problem driven by the Laplace operator plus an indefinite potential term. The reaction is of the logistic type. Using variational methods together with truncations, comparisons and critical groups, we prove two multiplicity theorems producing smooth solutions with sign information. A special case, which we encounter in the literature, is also considered.

Keywords

• Indefinite potential
• Robin boundary condition
• truncations
• Hopf maximum principle
• constant sign and nodal solutions
• critical groups