{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:35:27Z","timestamp":1760240127175,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T00:00:00Z","timestamp":1550793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We investigate the solvability and Ulam stability for a nonlocal nonlinear third-order integro-multi-point boundary value problem on an arbitrary domain. The nonlinearity in the third-order ordinary differential equation involves the unknown function together with its first- and second-order derivatives. Our main results rely on the modern tools of functional analysis and are well illustrated with the aid of examples. An analogue problem involving non-separated integro-multi-point boundary conditions is also discussed.<\/jats:p>","DOI":"10.3390\/sym11020281","type":"journal-article","created":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T03:49:44Z","timestamp":1550807384000},"page":"281","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Existence Theory for Nonlinear Third-Order Ordinary Differential Equations with Nonlocal Multi-Point and Multi-Strip Boundary Conditions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3452-8922","authenticated-orcid":false,"given":"Ahmed","family":"Alsaedi","sequence":"first","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"given":"Mona","family":"Alsulami","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5350-2977","authenticated-orcid":false,"given":"Bashir","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"},{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,22]]},"reference":[{"key":"ref_1","unstructured":"Zheng, L., and Zhang, X. (2017). Modeling and Analysis of Modern Fluid Problems. Mathematics in Science and Engineering, Elsevier\/Academic Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2919","DOI":"10.1016\/j.nonrwa.2011.02.017","article-title":"Van Gorder, Existence results for third order nonlinear boundary value problems arising in nano boundary layer fluid flows over stretching surfaces","volume":"12","author":"Akyildiz","year":"2011","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.jmmm.2016.02.017","article-title":"On magnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet","volume":"408","author":"Hayat","year":"2016","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1016","DOI":"10.1016\/j.ijmecsci.2017.08.022","article-title":"On analysis of magneto Maxwell nano-material by surface with variable thickness","volume":"131\u2013132","author":"Hayat","year":"2017","journal-title":"Int. J. Mech. Sci."},{"key":"ref_5","first-page":"294","article-title":"The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition","volume":"13","author":"Ionkin","year":"1977","journal-title":"Differ. Uravn."},{"key":"ref_6","first-page":"803","article-title":"Nonlocal boundary-value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects","volume":"23","author":"Moiseev","year":"1987","journal-title":"Diff. Equa."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.aml.2004.05.009","article-title":"Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions","volume":"18","author":"Eloe","year":"2005","journal-title":"Appl. Math. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1112\/S0024610706023179","article-title":"Positive solutions of nonlocal boundary value problems: A unified approach","volume":"74","author":"Webb","year":"2006","journal-title":"J. London Math. Soc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3363","DOI":"10.1090\/S0002-9939-06-08368-7","article-title":"Uniqueness implies existence and uniqueness criterion for non local boundary value problems for third-order differential equations","volume":"134","author":"Clark","year":"2006","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1542","DOI":"10.1016\/j.na.2008.12.047","article-title":"Third order boundary value problems with nonlocal boundary conditions","volume":"71","author":"Graef","year":"2009","journal-title":"Nonlinear Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/S0045-7825(98)80008-X","article-title":"Finite element modeling of blood flow in arteries","volume":"158","author":"Taylor","year":"1998","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1002\/fld.299","article-title":"Integral boundary conditions for unsteady biomedical CFD applications","volume":"40","author":"Nicoud","year":"2002","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1016\/j.nonrwa.2007.05.005","article-title":"Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions","volume":"9","author":"Ahmad","year":"2008","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.camwa.2012.02.031","article-title":"A study of higher-order nonlinear ordinary differential equations with four-point nonlocal integral boundary conditions","volume":"39","author":"Ahmad","year":"2012","journal-title":"J. Appl. Math. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"396","DOI":"10.15388\/NA.2014.3.6","article-title":"Smoothness of solutions with respect to multi-strip integral boundary conditions for nth order ordinary differential equations","volume":"19","author":"Henderson","year":"2014","journal-title":"Nonlinear Anal. Model. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2149","DOI":"10.2298\/FIL1410149A","article-title":"Existence of solutions or nonlinear nth-order differential equations and inclusions with nonlocal and integral boundary conditions via fixed point theory","volume":"28","author":"Ahmad","year":"2014","journal-title":"Filomat"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"188","DOI":"10.3846\/13926292.2015.1020531","article-title":"Positive solutions of nth-order boundary value problems with integral boundary conditions","volume":"20","author":"Karaca","year":"2015","journal-title":"Math. Model. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s10986-016-9311-6","article-title":"On higher-order nonlinear boundary value problems with nonlocal multipoint integral boundary conditions","volume":"56","author":"Ahmad","year":"2016","journal-title":"Lith. Math. J."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Boukrouche, M., and Tarzia, D.A. (2018). A family of singular ordinary differential equations of the third order with an integral boundary condition. Bound. Value Probl., 32.","DOI":"10.1186\/s13661-018-0950-x"},{"key":"ref_20","first-page":"303","article-title":"Diffraction of a plane wave by an elastic knife-edge adjacent to a rigid strip","volume":"9","author":"Ahmad","year":"2001","journal-title":"Canad. Appl. Math. Quart."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1016\/0013-7944(91)90148-T","article-title":"A strip model for fatigue crack growth predictions under general load conditions","volume":"40","author":"Wang","year":"1991","journal-title":"Eng. Fract. Mech."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2750","DOI":"10.1016\/j.jfranklin.2012.09.001","article-title":"A mixed boundary value problem in orthotropic strip containing a crack","volume":"349","author":"Yusufoglu","year":"2012","journal-title":"J. Franklin Inst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2404","DOI":"10.1016\/j.jsv.2012.01.006","article-title":"Road traffic noise shielding by vegetation belts of limited depth","volume":"331","author":"Renterghem","year":"2012","journal-title":"J. Sound Vib."},{"key":"ref_24","unstructured":"Smart, D.R. (2005). Fixed Point Theorems, Cambridge Tracts in Mathematics."},{"key":"ref_25","unstructured":"Granas, A., and Dugundji, J. (2005). Fixed Point Theory, Springer."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/281\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:34:02Z","timestamp":1760186042000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/2\/281"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,22]]},"references-count":25,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["sym11020281"],"URL":"https:\/\/doi.org\/10.3390\/sym11020281","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,2,22]]}}}