Breather solutions for a semilinear Klein-Gordon equation on a periodic metric graph
نویسندگان
چکیده
We consider the nonlinear Klein-Gordon equation∂t2u(x,t)−∂x2u(x,t)+αu(x,t)=±|u(x,t)|p−1u(x,t) on a periodic metric graph (necklace graph) for p>1 with Kirchhoff conditions at vertices. Under suitable assumptions frequency we prove existence and regularity of infinitely many spatially localized time-periodic solutions (breathers) by variational methods. Compared to previous results obtained via spatial dynamics center manifold techniques our provide all values α≥0 as well multiplicity. Moreover, deduce properties show that they are weak corresponding initial value problem. Our approach relies critical points indefinite functionals, concentration compactness principle, proper set-up functional analytic framework. earlier work breathers using techniques, major improvement embedding has been achieved. This allows in particular avoid restrictions exponent achieve higher regularity.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2023
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2023.127520