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A degree theory framework for semilinear elliptic systems


Authors: Congming Li and John Villavert
Journal: Proc. Amer. Math. Soc. 144 (2016), 3731-3740
MSC (2010): Primary 35B08, 35B09, 35J47, 35J61
DOI: https://doi.org/10.1090/proc/13166
Published electronically: April 28, 2016
MathSciNet review: 3513534
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Abstract: This paper establishes the existence of positive entire solutions to some systems of semilinear elliptic systems including those related to the Lane-Emden and stationary Schrödinger systems. The primary technique for generating these results employs a degree theoretic approach for the classical shooting method.


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Additional Information

Congming Li
Affiliation: Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309
Email: congming.li@colorado.edu

John Villavert
Affiliation: School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas 78539
Email: john.villavert@utrgv.edu, john.villavert@gmail.com

DOI: https://doi.org/10.1090/proc/13166
Keywords: Existence, ground state solution, Lane-Emden system, Schr\"odinger system, the shooting method, topological degree theory
Received by editor(s): September 11, 2015
Published electronically: April 28, 2016
Additional Notes: The first author is partially supported by NSF DMS-1405175 and NSFC-11571233
Communicated by: Catherine Sulem
Article copyright: © Copyright 2016 American Mathematical Society