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BOUNDARY VALUE PROBLEMS VIA AN INTERMEDIATE VALUE THEOREM
Published online by Cambridge University Press: 01 September 2008
Abstract
We use an intermediate value theorem for quasi-monotone increasing functions to prove the existence of the smallest and the greatest solution of the Dirichlet problem u″ + f(t, u) = 0, u(0) = α, u(1) = β between lower and upper solutions, where f:[0,1] × E → E is quasi-monotone increasing in its second variable with respect to a regular cone.
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- Copyright © Glasgow Mathematical Journal Trust 2008