Multiple positive solutions for a nonlinear Schrödinger equation
The authors investigate the number of positive solutions of the nonlinear Schrödinger equation \(-\Delta u+(\lambda a(x)+ 1)u= u^p\) in \(\mathbb{R}^N\), where \(a\geq 0\) has \(\text{int }a^{-1}(0)\) nonempty and \(p> 1\) is subcritical. The existence of multiple positive solutions is proved for \(\lambda\) sufficiently large by using variational methods.
existence of multiple positive solutions
scientific article; zbMATH DE number 1484707