Ljusternik-Schnirelman theory in partially ordered Hilbert spaces
Shujie Li, Zhi-Qiang Wang · Transactions of the American Mathematical Society · 2002
We present several variants of Ljusternik-Schnirelman type theorems in partially ordered Hilbert spaces, which assert the locations of the critical points constructed by the minimax method in terms of the order structures. These results are applied to nonlinear Dirichlet boundary value problems to obtain the multiplicity of sign-changing solutions.