A local min-max-orthogonal method for finding multiple solutions to noncooperative elliptic systems
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- by Xianjin Chen and Jianxin Zhou PDF
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Abstract:
A local min-max-orthogonal method together with its mathematical justification is developed in this paper to solve noncooperative elliptic systems for multiple solutions in an order. First it is discovered that a noncooperative system has the nature of a zero-sum game. A new local characterization for multiple unstable solutions is then established, under which a stable method for multiple solutions is developed. Numerical experiments for two types of noncooperative systems are carried out to illustrate the new characterization and method. Several important properties for the method are explored or verified. Multiple numerical solutions are found and presented with their profiles and contour plots. As a new bifurcation phenomenon, multiple asymmetric positive solutions to the second type of noncooperative systems are discovered numerically but are still open for mathematical verification.References
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Additional Information
- Xianjin Chen
- Affiliation: Institute for Mathematics & Its Application, University of Minnesota, Minneapolis, Minnesota 55455
- Email: xchen@ima.umn.edu
- Jianxin Zhou
- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- Email: jzhou@math.tamu.edu
- Received by editor(s): January 27, 2009
- Received by editor(s) in revised form: August 1, 2009
- Published electronically: March 26, 2010
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 2213-2236
- MSC (2010): Primary 35A15, 58E05, 58E30
- DOI: https://doi.org/10.1090/S0025-5718-10-02336-7
- MathSciNet review: 2684362