Multiple existence of sign changing solutions for a nonlinear elliptic problem (Q2474338)

Using critical point arguments the author proves the existence of at least seven pairs of sign changing solutions to the elliptic problem \(-\varepsilon ^{2}\Delta u+u=| u| ^{p-2}u,\) \(u\in H_{0}^{1}(\Omega)\) (\(2<p<2^{\ast },\) \(\varepsilon >0\)) under conditions on the shape of the domain \(\Omega .\)