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Jinguo Zhang

Publications and source records attributed to Jinguo Zhang.

7 recordsLinked to original sources
arXiv2025

ECVL-ROUTER: Scenario-Aware Routing for Vision-Language Models

Vision-Language Models (VLMs) excel in diverse multimodal tasks. However, user requirements vary across scenarios, which can be categorized into fast response, high-quality output, and low energy consumption. Relying solely on large models deployed in the cloud for all queries often leads to high latency and energy cost, while small models deployed on edge devices are capable of handling simpler tasks with low latency and energy cost. To fully leverage the strengths of both large and small models, we propose ECVL-ROUTER, the first scenario-aware routing framework for VLMs. Our approach introduces a new routing strategy and evaluation metrics that dynamically select the appropriate model for each query based on user requirements, maximizing overall utility. We also construct a multimodal response-quality dataset tailored for router training and validate the approach through extensive experiments. Results show that our approach successfully routes over 80\% of queries to the small model while incurring less than 10\% drop in problem solving probability.

cs.LG↗
arXiv2015

Existence and multiplicity results for the fractional Schrodinger-Poisson systems

This paper is devoted to study the existence and multiplicity solutions for the nonlinear Schrödinger-Poisson systems involving fractional Laplacian operator: \begin{equation}\label{eq*} \left\{ \aligned &(-Δ)^{s} u+V(x)u+ ϕu=f(x,u), \quad &\text{in }\mathbb{R}^3, &(-Δ)^{t} ϕ=u^2, \quad &\text{in }\mathbb{R}^3, \endaligned \right. \end{equation} where $(-Δ)^α$ stands for the fractional Laplacian of order $α\in (0\,,\,1)$. Under certain assumptions on $V$ and $f$, we obtain infinitely many high energy solutions for \eqref{eq*} without assuming the Ambrosetti-Rabinowitz condition by using the fountain theorem.

math.AP↗
arXiv2015

Existence and concentration of solutions for a fractional Schrodinger equations with sublinear nonlinearity

This article concerns the fractional elliptic equations \begin{equation*}(-Δ)^{s}u+λV(x)u=f(u), \quad u\in H^{s}(\mathbb{R}^N), \end{equation*}where $(-Δ)^{s}$ ($s\in (0\,,\,1)$) denotes the fractional Laplacian, $λ>0$ is a parameter, $V\in C(\mathbb{R}^N)$ and $V^{-1}(0)$ has nonempty interior. Under some mild assumptions, we establish the existence of nontrivial solutions. Moreover, the concentration of solutions is also explored on the set $V^{-1}(0)$ as $λ\to\infty$.

math.AP↗
arXiv2015

Multiplicity of positive solutions for a fractional Laplacian equations involving critical nonlinearity

In this paper we deal with the multiplicity of positive solutions to the fractional Laplacian equation \begin{equation*} (-Δ)^{\fracα{2}} u=λf(x)|u|^{q-2}u+|u|^{2^{*}_α-2}u, \quad\text{in}\,\,Ω, u=0,\text{on}\,\,\partialΩ, \end{equation*} where $Ω\subset \mathbb{R}^{N}(N\geq 2)$ is a bounded domain with smooth boundary, $0<α<2$, $(-Δ)^{\fracα{2}}$ stands for the fractional Laplacian operator, $f\in C(Ω\times\mathbb{R},\mathbb{R})$ may be sign changing and $λ$ is a positive parameter. We will prove that there exists $λ_{*}>0$ such that the problem has at least two positive solutions for each $λ\in (0\,,\,λ_{*})$. In addition, the concentration behavior of the solutions are investigated.

math.AP↗
arXiv2014

Arbitrary many positive solutions for a nonlinear problem involving the fractional Laplacian

We establish the existence and multiplicity of positive solutions to the problems involving the fractional Laplacian: \begin{equation*} \left\{\begin{array}{lll} &(-Δ)^{s}u=λu^{p}+f(u),\,\,u>0 \quad &\mbox{in}\,\,Ω,\\ &u=0\quad &\mbox{in}\,\,\mathbb{R}^{N}\setminusΩ,\\ \end{array}\right. \end{equation*} where $Ω\subset \mathbb{R}^{N}$ $(N\geq 2)$ is a bounded smooth domain, $s\in (0,1)$, $p>0$, $λ\in \mathbb{R}$ and $(-Δ)^{s}$ stands for the fractional Laplacian. When $f$ oscillates near the origin or at infinity, via the variational argument we prove that the problem has arbitrarily many positive solutions and the number of solutions to problem is strongly influenced by $u^{p}$ and $λ$. Moreover, various properties of the solutions are also described in $L^{\infty}$- and $X^{s}_{0}(Ω)$-norms.

math.AP↗