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Construction of upper and lower solutions for a problem in combustion theory

✍ Scribed by K.K Tam


Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
644 KB
Volume
69
Category
Article
ISSN
0022-247X

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πŸ“œ SIMILAR VOLUMES


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✍ Ravi P. Agarwal; Donal O'Regan πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 87 KB πŸ‘ 2 views

An upper and lower solution theory is presented for singular initial value problems. Our non-linear term may be singular in both the independent and dependent variable. Existence will be established using Schauder's "xed point theorem and the Arzela}Ascoli theorem.

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We prove the solvability of the Dirichlet-periodic problem for a semilinear parabolic equation, assuming the existence of a lower solution : and an upper solution ;, which do not satisfy the ordering condition : ;. Our results yield the existence of unstable solutions, localized by means of : and ;,