Critical scattering in a time-dependent harmonic oscillator
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DOI: 10.1016/j.jmaa.2020.124475
Abstract: Abstract Controlled time-decaying harmonic oscillator changes the threshold of decay order of the potential functions in order to exist the physical wave operators. This threshold was first reported by Ishida and Kawamoto [6] for the… read more here.
Keywords: time; case; harmonic oscillator; critical case ... See more keywords
Stability for a delayed switched nonlinear system of differential equations in a critical case
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DOI: 10.1080/00207179.2020.1862423
Abstract: In this paper the stability of an equilibrium of a feedback nonlinear system with time delay and structural switching is studied. The critical case of a zero root of the characteristic equations of... read more here.
Keywords: nonlinear system; critical case; stability delayed;
Limit-periodic solutions of integro-differential equations in a critical case
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DOI: 10.1134/s0012266117090099
Abstract: We consider equations with nonlinear terms representable by power series in the variable and functionals in integral form. The equation depends on a small exponentially limitperiodic perturbation, i.e., on a function that exponentially tends to… read more here.
Keywords: critical case; periodic solutions; limit periodic; differential equations ... See more keywords
On well-posedness for inhomogeneous Hartree equations in the critical case
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DOI: 10.3934/cpaa.2023060
Abstract: We study the well-posedness for the inhomogeneous Hartree equation $i\partial_t u + \Delta u = \lambda(I_\alpha \ast |\cdot|^{-b}|u|^p)|x|^{-b}|u|^{p-2}u$ in $H^s$, $s\ge0$. Until recently, its well-posedness theory has been intensively studied, focusing on solving the problem… read more here.
Keywords: inhomogeneous hartree; hartree equations; critical case; case ... See more keywords