Multiplicity results for weak solutions of a semilinear Dirichlet elliptic problem with a parametric nonlinearity (Q2691633)

Summary: This paper deals with the existence of weak solutions to a Dirichlet problem for a semilinear elliptic equation involving the difference of two main nonlinearities functions that depends on a real parameter \(\lambda \). According to the values of \(\lambda \), we give both nonexistence and multiplicity results by using variational methods. In particular, we first exhibit a critical positive value such that the problem admits at least a nontrivial non-negative weak solution if and only if \(\lambda\) is greater than or equal to this critical value. Furthermore, for \(\lambda\) greater than a second critical positive value, we show the existence of two independent nontrivial non-negative weak solutions to the problem.