Singular semi-linear equations inL
1(R) |
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Authors: | Stephen D Fisher |
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Institution: | (1) Mathematics Research Center, University of Wisconsin, Madison;(2) Northwestern University, Evanston, Ill. |
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Abstract: | Letg be a positive continuous function onR which tends to zero at −∞ and which is not integrable overR. The boundary-value problem −u″+g(u)=f, u′(±∞)=0, is considered forf∈L
1(R). We show that this problem can have a solution if and only ifg is integrable at −∞ and if this is so then the problem is solvable precisely when ∫
−∞
∞
. Some extensions of this result are also given.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and by the National Science Foundation, Grant MPS
75-05501. |
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Keywords: | |
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