Conley indices on convex sets, attractor-repeller pairs and applications to multiple solutions of nonlinear elliptic equations |
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Authors: | E. N. Dancer |
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Affiliation: | (1) School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia |
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Abstract: | We discuss the calculation of homotopy indices on closed convex sets in a Banach space and then use these ideas to prove the existence of multiple solutions of nonlinear elliptic equations. We obtain more information on the solutions than in earlier work. A key idea is to calculate the homotopy index of the stable and mountain pass solutions and the connections joining them. Dedicated to the memory of Jean Leray |
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Keywords: | Primary 35J65 |
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