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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A singular semilinear equation in $L^{1}(\textbf {R})$
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by Michael G. Crandall and Lawrence C. Evans PDF
Trans. Amer. Math. Soc. 225 (1977), 145-153 Request permission

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
  • © Copyright 1977 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 225 (1977), 145-153
  • MSC: Primary 34B15
  • DOI: https://doi.org/10.1090/S0002-9947-1977-0477240-0
  • MathSciNet review: 0477240