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Conley indices on convex sets, attractor-repeller pairs and applications to multiple solutions of nonlinear elliptic equations

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia

    E. N. Dancer

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  1. E. N. Dancer
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Correspondence to E. N. Dancer.

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Dedicated to the memory of Jean Leray

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Dancer, E.N. Conley indices on convex sets, attractor-repeller pairs and applications to multiple solutions of nonlinear elliptic equations. J.fixed point theory appl. 1, 47–60 (2007). https://doi.org/10.1007/s11784-006-0003-4

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  • DOI: https://doi.org/10.1007/s11784-006-0003-4

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