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In this paper, we investigate the existence of a set with 2kT$2kT$-periodic solutions for n-dimensional p-Laplacian neutral differential systems with a time-varying delay (φp(u(t)−Cu(t−τ))′)′+ddt∇F(u(t))+G(u(t−γ(t)))=ek(t)$(\varphi_{p}(u(t)-Cu(t-\tau ))')'+ \frac{d}{dt}\nabla F(u(t))+G(u(t-\gamma (t)))=e_{k}(t)$ based on… Click to show full abstract
In this paper, we investigate the existence of a set with 2kT$2kT$-periodic solutions for n-dimensional p-Laplacian neutral differential systems with a time-varying delay (φp(u(t)−Cu(t−τ))′)′+ddt∇F(u(t))+G(u(t−γ(t)))=ek(t)$(\varphi_{p}(u(t)-Cu(t-\tau ))')'+ \frac{d}{dt}\nabla F(u(t))+G(u(t-\gamma (t)))=e_{k}(t)$ based on the coincidence degree theory of Mawhin. Combining this with the conclusion about uniform convergence and limit, we obtain the corresponding results on the existence of homoclinic solutions.
Journal Title: Advances in Difference Equations
Year Published: 2018
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