Let [tex] f \in \mathcal{C}(\mathbb{R})[/tex] be a continuous function such that [tex] tf(t) \geq 0[/tex] [tex]\forall t [/tex]. I must prove that(adsbygoogle = window.adsbygoogle || []).push({});

[tex] y''+e^{-x}f(y)=0 [/tex]

[tex] y(0)=y'(0)=0 [/tex]

has [tex] y \equiv 0 [/tex] as unique solution. No idea whatsoever up to this moment, so... thanks in adv.

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# Constant solution

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