Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity
We study the existence, nonexistence and multiplicity of positive solutions for the family of problems , , where is a bounded domain in , and is a parameter. The results include the well-known nonlinearities of the Ambrosetti–Brezis–Cerami type in a more general form, namely , where . The coefficient is assumed to be nonnegative but is allowed to change sign, even in the critical case. The notions of local superlinearity and local sublinearity introduced in [9] are essential in this...