Periodic Solutions of Asymptotically Linear Autonomous Hamiltonian Systems with Resonance
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DOI: 10.1007/s10884-017-9608-0
Abstract: In this paper we define the index at infinity of an asymptotically linear autonomous Hamiltonian system. We use this index to prove the existence and bifurcation from infinity of periodic solutions of the system. We… read more here.
Keywords: periodic solutions; asymptotically linear; linear autonomous; solutions asymptotically ... See more keywords
Nehari Type Ground State Solutions for Asymptotically Periodic Schrödinger-Poisson Systems
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DOI: 10.11650/tjm/7784
Abstract: This paper is dedicated to studying the following Schrodinger-Poisson system\[ \begin{cases} -\Delta u + V(x)u + K(x) \phi(x)u = f(x,u), x t > 0, \; \tau \neq 0\]with constant $\theta_0 \in (0,1)$, instead of $\lim_{|t|… read more here.
Keywords: type ground; nehari type; poisson; state solutions ... See more keywords
Ground state solutions for asymptotically periodic Schrödinger–Poisson systems involving Hartree-type nonlinearities
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DOI: 10.1186/s13661-018-1025-8
Abstract: AbstractWe use the non-Nehari manifold method to deal with the system {−Δu+V(x)u+ϕu=(∫R3Q(y)F(u(y))|x−y|μdy)Q(x)f(u(x)),x∈R3,−Δϕ=u2,u∈H1(R3),$$ \textstyle\begin{cases} -\Delta u+V(x)u+\phi u= (\int_{\mathbb{R}^{3}}\frac {Q(y)F(u(y))}{|x-y|^{\mu}}\,dy )Q(x)f(u(x)),\quad x\in\mathbb{R}^{3}, \\ -\Delta\phi=u^{2}, \quad u \in H^{1}(\mathbb{R}^{3}), \end{cases} $$ where V(x)$V(x)$ and Q(x)$Q(x)$ are periodic and… read more here.
Keywords: asymptotically periodic; state solutions; solutions asymptotically; type ... See more keywords