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Existence of periodic solutions of semilinear parabolic equations and the method of upper and lower solutions

โœ Scribed by R Kannan; V Lakshmikantham


Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
415 KB
Volume
97
Category
Article
ISSN
0022-247X

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The existence and multiplicity results of solutions are obtained by the reduction method and the minimax methods for nonautonomous semilinear elliptic Dirichlet boundary value problem. Some well-known results are generalized. แฎŠ 2001 Aca- demic Press

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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 ;,