Existence of solutions of 𝑥”+𝑥+𝑔(𝑥)=𝑝(𝑡),𝑥(0)=0=𝑥(𝜋)

Kannan, R.; Ortega, R.

doi:10.1090/S0002-9939-1986-0813812-X

Existence of solutions of $x”+x+g(x)=p(t),\;x(0)=0=x(\pi )$
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by R. Kannan and R. Ortega PDF

Proc. Amer. Math. Soc. 96 (1986), 67-70 Request permission

Abstract:

We obtain criteria for the existence of solutions of $x + x + g(x) = p(t),x(0) = 0 = x(\pi )$, where $g:R \to R$ is not necessarily bounded and does not necessarily have proper limits $g(\infty )$ and $g( - \infty )$.

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