{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T00:38:53Z","timestamp":1773103133621,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T00:00:00Z","timestamp":1772841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study a fractional Kirchhoff problem with a Hardy-type singular potential and general nonlinearities depending on the solution and its gradient: M\u222b\u222bRN\u00d7RN|u(x)\u2212u(y)|q|x\u2212y|N+qsdxdy(\u2212\u0394)su=\u03bbu|x|2s+f(x,u,\u2207u)in\u03a9, where \u03a9\u2282RN is a bounded domain containing the origin, s\u2208(0,1), q\u2208(1,2] with N&gt;2s, \u03bb&gt;0, and f is a measurable non-negative function satisfying suitable hypotheses. The main objective is to establish the existence of positive solutions for the largest possible class of nonlinearities f without imposing restrictions on \u03bb. Two main cases areconsidered: (I)\u2212f(x,u,\u2207u)=up+\u03bc,and(II)\u2212f(x,u,\u2207u)=|\u2207u|p+\u03bcg. Existence is proved under suitable hypotheses on q,p and the data g,\u03bc. The results are new, including for the local case s=1.<\/jats:p>","DOI":"10.3390\/axioms15030199","type":"journal-article","created":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T08:58:45Z","timestamp":1773046725000},"page":"199","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fractional Kirchhoff-Hardy Problem: Breaking of Resonance and General Existence Results"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8232-1403","authenticated-orcid":false,"given":"Boumediene","family":"Abdellaoui","sequence":"first","affiliation":[{"name":"Laboratoire d\u2019Analyse Nonlin\u00e9aire et Math\u00e9matiques Appliqu\u00e9s, D\u00e9partement de Math\u00e9matiques, Universit\u00e9 Aboubekr Belka\u00efd, Tlemcen 13000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0960-7768","authenticated-orcid":false,"given":"Abdelhalim","family":"Azzouz","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Math\u00e9matique, Facult\u00e9 de Math\u00e9matique, Informatique et T\u00e9l\u00e9communications, Universit\u00e9 Dr Moulay Tahar, Saida 20000, Algeria"}]},{"given":"Ahmed","family":"Bensedik","sequence":"additional","affiliation":[{"name":"Laboratoire Systeme dynamiques et applications, D\u00e9partement de Math\u00e9matiques, Universit\u00e9 Abou Bakr Belka\u00efd, Tlemcen 13000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3177-663X","authenticated-orcid":false,"given":"Rachid","family":"Bentifour","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Analyse Nonlin\u00e9aire et Math\u00e9matiques Appliqu\u00e9s, D\u00e9partement de Math\u00e9matiques, Universit\u00e9 Aboubekr Belka\u00efd, Tlemcen 13000, Algeria"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,7]]},"reference":[{"key":"ref_1","first-page":"1897","article-title":"Pitt\u2019s inequality and the uncertainty principle","volume":"123","author":"Beckner","year":"1995","journal-title":"Proc. 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