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$2\pi$-Periodic self-similar solutions for the anisotropic affine curve shortening problem II

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  • The existence of $2\pi$-periodic positive solutions of the equation $$ u'' + u = \displaystyle{\frac{a(x)}{u^3}} $$ is studied, where $a$ is a positive smooth $2\pi$-periodic function. Under some non-degenerate conditions on $a$, the existence of $2\pi$-periodic solutions to the equation is established.
    Mathematics Subject Classification: Primary: 34B15, 34B16; Secondary: 44J99.


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