Nodal solutions for some singularly perturbed Dirichlet problems
Teresa D’Aprile, Angela Pistoia · Transactions of the American Mathematical Society · 2011
We consider the equation $-\varepsilon ^2 \Delta u+u=f(u)$ in a bounded, smooth domain $\Omega \subset \Bbb R^N$ with homogeneous Dirichlet boundary conditions. We prove the existence of nodal solutions with multiple peaks concentrating at different points of $\Omega$. The nonlinearity $f$ grows superlinearly and subcritically. We do not require symmetry conditions on the geometry of the domain.