{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:07:33Z","timestamp":1760058453275,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T00:00:00Z","timestamp":1744243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007414","name":"Deanship of Scientific Research, Qassim University","doi-asserted-by":"publisher","award":["QU-J-PG-2-2025-53930"],"award-info":[{"award-number":["QU-J-PG-2-2025-53930"]}],"id":[{"id":"10.13039\/501100007414","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we consider the nonlinear elliptic equation \u2212\u0394u+V(x)u=g(x)un+2n\u22122\u2212\u03b5 in a bounded, smooth domain \u03a9 in Rn, under zero Neumann boundary conditions, where n\u22654, \u03b5 is a small positive parameter, and V and g are non-constant smooth positive functions on \u03a9\u00af. Under certain flatness conditions on the function g, we provide a complete description of the single interior blow-up scenario for solutions that weakly converge to zero. We also construct interior multipeaked solutions, both with isolated and clustered bubbles. The proofs of our results rely on a refined asymptotic expansion of the gradient of the corresponding functional. Furthermore, no assumption regarding the symmetry of the domain is required.<\/jats:p>","DOI":"10.3390\/sym17040579","type":"journal-article","created":{"date-parts":[[2025,4,10]],"date-time":"2025-04-10T08:46:20Z","timestamp":1744274780000},"page":"579","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Interior Multipeaked Solutions for Slightly Subcritical Elliptic Problems"],"prefix":"10.3390","volume":"17","author":[{"given":"Abdulhadi","family":"Almoteri","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51542, Saudi Arabia"}]},{"given":"Khalil","family":"El Mehdi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51542, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/0022-5193(70)90092-5","article-title":"Initiation of slime mold aggregation viewed as an instability","volume":"26","author":"Keller","year":"1970","journal-title":"J. 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