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A Singular Semilinear Equation in L1(R)

Michael G. Crandall and Lawrence C. Evans
Transactions of the American Mathematical Society
Vol. 225 (Jan., 1977), pp. 145-153
DOI: 10.2307/1997497
Stable URL: http://www.jstor.org/stable/1997497
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Singular Semilinear Equation in L1(R)
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Abstract

Let β be a positive and nondecreasing function on R. The boundary-value problem β(u) - u" = f, u'(± ∞) = 0 is considered for f ∫ L1(R). It is shown that this problem can have a solution only if β is integrable near -∞, and that if this is the case, then the problem has a solution exactly when $\int^\infty_{-\infty}f(x)dx > 0$.

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