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Cartoon martian with big head

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We study the existence and multiplicity of homoclinic solutions for the second-order damped differential equation $$ \ddot{u}+c\dot{u}-L(t)u+W_u(t. u)=0. $$ where L(t) and W(t. u) are neither autonomous nor periodic in t. https://www.alarecre.com/Looney-Tunes-Marvin-the-Martian-Big-Head-Galaxy-S23-Waterproof-Case-p116784/

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