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MR813812 (87c:34026) 34B15 (47H15)
Kannan, R.; Ortega, R. Existence of solutions of $x''+x+g(x)=p(t),\;x(0)=0=x(\pi)$. Proc. Amer. Math. Soc. 96 (1986), no. 1, 67–70.
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