# American Institute of Mathematical Sciences

June  2010, 28(2): 809-826. doi: 10.3934/dcds.2010.28.809

## On a new index theory and non semi-trivial solutions for elliptic systems

 1 School of Mathematical Sciences, Peking University, Beijing 100871, China 2 Department of Mathematics and Statistics, Utah State University, Logan, UT 84322 3 Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, United States

Received  February 2010 Revised  April 2010 Published  April 2010

Two indices, which are similar to the Krasnoselski's genus on the sphere, are defined on the product of spheres. They are applied to investigate the multiple non semi-trivial solutions for elliptic systems. Both constraint and unconstraint problems are studied.
Citation: Kung-Ching Chang, Zhi-Qiang Wang, Tan Zhang. On a new index theory and non semi-trivial solutions for elliptic systems. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 809-826. doi: 10.3934/dcds.2010.28.809
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