arXiv subjects

Ashutosh Dixit

Publications and source records attributed to Ashutosh Dixit.

10 recordsLinked to original sources

arXiv2026

On polyharmonic Kirchhoff double phase problems without AR-conditions

In this paper, we study a class of polyharmonic Kirchhoff problems driven by a double phase operator. The reaction term has subcritical growth but does not satisfy the Ambrosetti--Rabinowitz condition. Motivated by the work of Harrabi-Hamdani-Fiscella \cite{Harrabi-Hamdani-Fiscella-2024} on m-polyharmonic Kirchhoff problems without Ambrosetti--Rabinowitz conditions, we extend their analysis to a nonhomogeneous double phase setting. We study the problem in the natural Musielak--Orlicz--Sobolev framework associated with the double phase structure. The main novelty of the paper lies in combining the nonlocal Kirchhoff term with a higher-order double phase operator under assumptions weaker than the classical Ambrosetti--Rabinowitz condition. By developing suitable modular estimates and compactness arguments, we establish the variational setting and obtain existence and multiplicity results by minimax methods.

math.AP↗

arXiv2026

On doubly critical polyharmonic double phase problems: Existence and non-existence of solutions

In this article, we investigate the existence and nonexistence of weak solutions to higher-order doubly critical elliptic problems with weights, driven by a polyharmonic double phase operator. More precisely, we deal with the following problem \begin{equation} \begin{cases} \mathcal{L}^m_{p,q}(u) = f(x,u) ~&\text{in } Ω,\\[6pt] u=\nabla u=\cdots\nabla^{m-1} u=0 &\text{on }{\partialΩ}, \end{cases} \end{equation} where $Ω\subset \mathbb{R}^N$ with $N \geq 2$ is a smooth bounded domain with Lipschitz boundary $\partialΩ$, $m \in \mathbb{N}$, $1 < p < q < \frac{N}{m}$ with $(N-1)q\leq Np$, the nonlinear term $f\colonΩ\times\mathbb{R}\to \mathbb{R}$ is a Carathéodory function, which has doubly critical growth, and $\mathcal{L}^m_{p,q}$ represents a polyharmonic double phase operator. By establishing new compactness results within a suitable Musielak--Orlicz--Sobolev framework and applying variational methods, we prove the existence of nontrivial weak solutions. In addition, we derive nonexistence results under appropriate assumptions by establishing a Pohozaev-type identity for higher--order derivatives. Our approach extends classical techniques to capture the intricate features of the double-phase operator for higher--order derivatives, and addresses the difficulties arising from critical nonlinearities, in particular extending the results of [F. Colasuonno, K. Perera, J. Differ. Equ., 422 (2025), 426--488] in a polyharmonic double phase setup overcoming the non-closedness of truncations in higher-order Sobolev spaces.

math.AP↗

arXiv2025

Non variational type critical growth nonlocal system

This study investigates the existence, uniqueness, and multiplicity of positive solutions for a system of fractional differential equations given by: \begin{equation*} (-Δ)^{s_i} u_{i}+λ_{i} u_{i}=\sum_{j=1}^{n} α_{i j}\left|u_{j}\right|^{q_{i j}}\left|u_{i}\right|^{p_{i j}-2} u_{i} , u_i\in {\mathscr{D}^{s_i,2}\left(\mathbb{R}^{N}\right)}, i=1,2,\cdots,n, \end{equation*} where $N>2s=\max\{2s_i\}$, $s_i\in(0,1)$, $n\geq 2$, $λ_{i} \geq 0$, $α_{ij}>0$, $p_{ij}<2^{*}_{s}$, and $p_{ij}+q_{ij}=2^{*}_{s}=\min\{{\frac{2N}{N-2s_i}\}}$ for $i\neq j \in \{1,2,...,n\}$. $2^{*}_s$ called the fractional critical sobolev exponent and $2^{*}_s=2 N /(N-2s)$ for $N > 2s$ and $2^{*}_s=+\infty$ for $N=2s$ or $N<2s$. Our work establishes novel uniqueness and multiplicity results for positive solutions, applicable whether the system possesses a variational structure or not. We provide a comprehensive characterization of the exact number of positive solutions under specific parameter configurations. Our analysis shows that the positive solution set behaves differently across three distinct regimes: $p_{ij}<2$, $p_{ij}=2$, and $2<p_{ij}<2^{*}_{s}$.

math.AP↗

arXiv2024

Existence of normalized ground state solution to a mixed Schrödinger system in a plane

In this paper, we establish the existence of positive ground state solutions for a class of mixed Schrödinger systems with concave-convex nonlinearities in $\mathbb{R}^2$, subject to $L^2$-norm constraints; that is, \[ \left\{ \begin{aligned} -\partial_{xx} u + (-Δ)_y^s u + λ_1 u &= μ_1 u^{p-1} + βr_1 u^{r_1-1} v^{r_2}, && -\partial_{xx} v + (-Δ)_y^s v + λ_2 v &= μ_2 v^{q-1} + βr_2 u^{r_1} v^{r_2-1}, && \end{aligned} \right. \] subject to the $L^2$-norm constraints: \[ \int_{\mathbb{R}^2} u^2 \,\mathrm{d}x\mathrm{d}y = a \quad \text{and} \quad \int_{\mathbb{R}^2} v^2 \,\mathrm{d}x\mathrm{d}y = b, \] where $(x,y)\in \mathbb{R}^2$, $u, v \geq 0$, $s \in \left(1/2, 1 \right)$, $μ_1, μ_2, β> 0$, $r_1, r_2 > 1$, the prescribed masses $a, b > 0$, and the parameters $λ_1, λ_2$ appear as Lagrange multipliers. Moreover, the exponents $p, q, r_1 + r_2$ satisfy: \[ \frac{2(1+3s)}{1+s} < p, q, r_1 + r_2 < 2_s, \] where $2_s = \frac{2(1+s)}{1-s}$. To obtain our main existence results, we employ variational techniques such as the Mountain Pass Theorem, the Pohozaev manifold, Steiner rearrangement, and others, consolidating the works of Louis Jeanjean et al. \cite{jeanjean2024normalized}.

math.AP↗

arXiv2015

URL ordering policies for distributed crawlers: a review

With the increase in size of web, the information is also spreading at large scale. Search Engines are the medium to access this information. Crawler is the module of search engine which is responsible for download the web pages. In order to download the fresh information and get the database rich, crawler should crawl the web in some order. This is called as ordering of URLs. URL ordering should be done in efficient and effective manner in order to crawl the web in proficient manner. In this paper, a survey is done on some existing methods of URL ordering and at the end of this paper comparison is also carried out among them.

cs.IR↗

arXiv2015

Design and Implementation of Domain based Semantic Hidden Web Crawler

Web is a wide term which mainly consists of surface web and hidden web. One can easily access the surface web using traditional web crawlers, but they are not able to crawl the hidden portion of the web. These traditional crawlers retrieve contents from web pages, which are linked by hyperlinks ignoring the information hidden behind form pages, which cannot be extracted using simple hyperlink structure. Thus, they ignore large amount of data hidden behind search forms. This paper emphasizes on the extraction of hidden data behind html search forms. The proposed technique makes use of semantic mapping to fill the html search form using domain specific database. Using semantics to fill various fields of a form leads to more accurate and qualitative data extraction.

cs.IR↗

arXiv2015

A novel design of hidden web crawler using ontology

Deep Web is content hidden behind HTML forms. Since it represents a large portion of the structured, unstructured and dynamic data on the Web, accessing Deep-Web content has been a long challenge for the database community. This paper describes a crawler for accessing Deep-Web using Ontologies. Performance evaluation of the proposed work showed that this new approach has promising results.

cs.IR↗

arXiv2013

A Novel Architecture for Relevant Blog Page Identifcation

Blogs are undoubtedly the richest source of information available in cyberspace. Blogs can be of various natures i.e. personal blogs which contain posts on mixed issues or blogs can be domain specific which contains posts on particular topics, this is the reason, they offer wide variety of relevant information which is often focused. A general search engine gives back a huge collection of web pages which may or may not give correct answers, as web is the repository of information of all kinds and a user has to go through various documents before he gets what he was originally looking for, which is a very time consuming process. So, the search can be made more focused and accurate if it is limited to blogosphere instead of web pages. The reason being that the blogs are more focused in terms of information. So, User will only get related blogs in response to his query. These results will be then ranked according to our proposed method and are finally presented in front of user in descending order

cs.IR↗

arXiv2013

A Novel Architecture For Question Classification Based Indexing Scheme For Efficient Question Answering

Question answering system can be seen as the next step in information retrieval, allowing users to pose question in natural language and receive compact answers. For the Question answering system to be successful, research has shown that the correct classification of question with respect to the expected answer type is requisite. We propose a novel architecture for question classification and searching in the index, maintained on the basis of expected answer types, for efficient question answering. The system uses the criteria for Answer Relevance Score for finding the relevance of each answer returned by the system. On analysis of the proposed system, it has been found that the system has shown promising results than the existing systems based on question classification.

cs.IR↗

arXiv2013

Presence Factor-Oriented Blog Summarization

The research that has been carried out on blogs focused on blog posts only, ignoring the title of the blog page. Also, in summarization only a set of representative sentences are extracted. Some analysis has been done and it has been found that the blog post contains the content that is likely to be related to the topic of the blog post. Thus, proposed system of summarization makes use of title contained in a blog page. The approach makes use of the Presence factor that indicates the presence of each term of the title in each sentence of the blog post. This is a key feature because it considers those sentences as more relevant for summarization that contain each of the term present in the title. The system has been implemented and evaluated experimentally. The system has shown promising results.

cs.IR↗