Nontrivial Periodic Solutions for Asymptotically Linear Hamiltonian Systems with Resonance

AbstractIn this paper, we establish some existence results of nontrivial 1-periodic solutions to the first-order asymptotically linear Hamiltonian systems, under the assumptions that the linear operators have different Maslove indices at the origin and at infinity. The results obtained in this paper are also valued for the case that both of the asymptotic matrices may be degenerate (resonant-type) and time dependent

Non-degeneracy of double-tower solutions for nonlinear Schr\"odinger equation and applications

This paper is concerned with the following nonlinear Schr\"odinger equation \begin{equation} \label{eq} - \Delta u + V(|y|)u=u^{p},\quad u>0 \ \ \mbox{in} \ \mathbb {R}^N, \ \ \ u \in H^1(\mathbb {R}^N), \end{equation} where $V(|y|)$ is a positive function, $1<p <\frac{N+2}{N-2}$. Based on the local Pohozaev identities and blow-up analysis, we first prove a non-degeneracy result for double-tower solutions constructed in [18] in a suitable symmetric space. As an application, we obtain the existence of new type solutions for (0.1).Comment: 34 pages, 0 figure

Screening for the optimal siRNA targeting a novel gene (HA117) and construction and evaluation of a derivative recombinant adenovirus

We found a novel gene named as HA117 in our previous research. At this study, we screened for an optimal siRNA targeting the novel gene HA117 using the pSOS-HUS method, verified the results of pSOS-HUS siRNA screening for optimal affinity for the target gene, and constructed and evaluated a recombinant adenovirus carrying the DNA template for transcription of the optimal HA117 siRNA. The pSOS-HUS vector method was successfully utilized as a rapid and effective screen for an optimal siRNA for a target gene. Among five pairs of DNA templates, siRNA transcribed from HAi5 gave the strongest interference with the novel gene HA117; a HAi5-carrying recombinant adenovirus (Ad-HAi5) was successfully constructed and evaluated, laying a foundation for the further study of HA117 gene function with RNAi technology

Double-tower Solutions for Higher Order Prescribed Curvature Problem

We consider the following higher order prescribed curvature problem on ${\mathbb{S}}^N :$ \begin{equation*} D^m \tilde u=\widetilde{K}(y) \tilde u^{m^{*}-1} \quad \mbox{on} \ {\mathbb {S}}^N, \qquad \tilde u >0 \quad \mbox{in} \ {\mathbb {S}}^N. \end{equation*} where $\widetilde{K}(y)>0$ is a radial function, $m^{*}=\frac{2N}{N-2m}$ and $D^m$ is $2m$ order differential operator given by \begin{equation*} D^m=\prod_{i=1}^m\left(-\Delta_g+\frac{1}{4}(N-2i)(N+2i-2)\right), \end{equation*} where $g=g_{{\mathbb{S}}^N}$is the Riemannian metric. We prove the existence of infinitely many double-tower type solutions, which are invariant under some non-trivial sub-groups of $O(3),$ and their energy can be made arbitrarily large.Comment: 34 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2205.14482 by other author