An Extension of the Hess-Kato Theorem to Elliptic Systems and Its Applications to Multiple Solution Problems

摘要

The Hess-Kato Theorem on the simplicity of the first eigenvalue of a second order elliptic operator is extended to elliptic systems. The theorem is applied to figure out the critical groups of a mountain pass point for functionals which have nonlinear ellipitic systems as Euler Lagrange Equations. A muliple solution result is obtained via the ordered Banach space method and the critical group calculations.