Global solution curves for semilinear systems
β Scribed by Philip Korman
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 135 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.273
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β¦ Synopsis
Abstract
We study semilinear elliptic systems in two different directions. In the first one we give a simple constructive proof existence of solutions for a class of sublinear systems. Our main results are in the second direction, where we use bifurcation theory to study global solution curves. Crucial to our analysis is proving positivity properties of the corresponding linearized systems. Copyright Β© 2002 John Wiley & Sons, Ltd.
π SIMILAR VOLUMES
We use bifurcation theory to study positive, negative, and sign-changing solutions for several classes of boundary value problems, depending on a real parameter . We show the existence of infinitely many points of pitchfork bifurcation, and study global properties of the solution curves.
A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.