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New Results for Some Neutral Partial Functional Differential Equations
Results in Mathematics, 2019The paper deals with the existence and uniqueness of doubly measures pseudo almost automorphic and pseudo almost periodic solutions for the following neutral equations in Hilbert space: \[\begin{array}{lll} \displaystyle \frac{d}{dt}\left[u(t)-G(t,u(k_1(t)))\right]&=&A\left[u(t)-G(t,u(k_1(t)))\right]+Bu(t)\\ &+& F-G(t,u(k_2(t))),\quad t\in \mathbb{R}, \
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Rotating Waves in Neutral Partial Functional Differential Equations
Journal of Dynamics and Differential Equations, 1999The local existence and global continuation of rotating waves for partial neutral functional differential equations \[ \frac{\partial }{\partial t}D(\alpha, u_t)=d\frac{\partial^2}{\partial x^2}D(\alpha,u_t)+f(\alpha,u_t)\tag{1} \] defined on the unit circle \(x\in S^1\) is investigated; where \(d>0\) is a given constant; \(D,\;f:\mathbb{R}\times X ...
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