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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A note on divergence-like $ 2$-point boundary value problems


Author: M. Joshi
Journal: Proc. Amer. Math. Soc. 42 (1974), 547-550
MSC: Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-1974-0328183-7
MathSciNet review: 0328183
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Abstract: The method given by Ford [1] for the existence and uniqueness of a solution in $ H_0^1(I)$ for the boundary value problem $ [h(x,x',t)]' = f(x,x',t), x(0) = x(1) = 0$ is shown to be a special case of Browder's method [3] for partial differential equations of generalized divergence form. Also it is shown that the solution of the above boundary value problem in $ H_0^{1,p}(I)$ can be obtained under weaker hypotheses than those assumed by Ford.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0328183-7
Article copyright: © Copyright 1974 American Mathematical Society