Abstract
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.
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Chang, K. An extension of the Hess-Kato Theorem to elliptic systems and its applications to multiple solution problems. Acta Math Sinica 15, 439–454 (1999). https://doi.org/10.1007/s10114-999-0078-0
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DOI: https://doi.org/10.1007/s10114-999-0078-0