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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A singular semilinear equation in $ L\sp{1}({\bf R})$


Authors: Michael G. Crandall and Lawrence C. Evans
Journal: Trans. Amer. Math. Soc. 225 (1977), 145-153
MSC: Primary 34B15
MathSciNet review: 0477240
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Abstract: Let $ \beta $ be a positive and nondecreasing function on R. The boundary-value problem $ \beta (u) - u'' = f,u'( \pm \infty ) = 0$ is considered for $ f \in {L^1}({\mathbf{R}})$. It is shown that this problem can have a solution only if $ \beta $ is integrable near $ - \infty $, and that if this is the case, then the problem has a solution exactly when $ \smallint _{ - \infty }^\infty f(x)dx > 0$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0477240-0
PII: S 0002-9947(1977)0477240-0
Keywords: Nonlinear boundary value problem, accretive operator
Article copyright: © Copyright 1977 American Mathematical Society