{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T01:51:02Z","timestamp":1768096262752,"version":"3.49.0"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,5,20]],"date-time":"2014-05-20T00:00:00Z","timestamp":1400544000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/2.0"},{"start":{"date-parts":[[2014,5,20]],"date-time":"2014-05-20T00:00:00Z","timestamp":1400544000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bound Value Probl"],"published-print":{"date-parts":[[2014,12]]},"abstract":"Abstract<\/jats:title>\n We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem \n \n \n \n (<\/mml:mo>\n \n u<\/mml:mi>\n \u2032<\/mml:mo>\n <\/mml:msup>\n \/<\/mml:mo>\n \n \n 1<\/mml:mn>\n +<\/mml:mo>\n \n u<\/mml:mi>\n \n \u2032<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:msqrt>\n )<\/mml:mo>\n <\/mml:mrow>\n \u2032<\/mml:mo>\n <\/mml:msup>\n =<\/mml:mo>\n a<\/mml:mi>\n u<\/mml:mi>\n \u2212<\/mml:mo>\n b<\/mml:mi>\n \/<\/mml:mo>\n \n \n 1<\/mml:mn>\n +<\/mml:mo>\n \n u<\/mml:mi>\n \n \u2032<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:mrow>\n <\/mml:msqrt>\n <\/mml:math>\n <\/jats:inline-formula> in \n \n [<\/mml:mo>\n 0<\/mml:mn>\n ,<\/mml:mo>\n 1<\/mml:mn>\n ]<\/mml:mo>\n <\/mml:math>\n <\/jats:inline-formula>, \n \n \n u<\/mml:mi>\n \u2032<\/mml:mo>\n <\/mml:msup>\n (<\/mml:mo>\n 0<\/mml:mn>\n )<\/mml:mo>\n =<\/mml:mo>\n u<\/mml:mi>\n (<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n =<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:math>\n <\/jats:inline-formula>, for any given \n \n a<\/mml:mi>\n ><\/mml:mo>\n 0<\/mml:mn>\n <\/mml:math>\n <\/jats:inline-formula> and \n \n b<\/mml:mi>\n ><\/mml:mo>\n 0<\/mml:mn>\n <\/mml:math>\n <\/jats:inline-formula>. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasi\u0144ski and P\u0142ociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.<\/jats:p>","DOI":"10.1186\/1687-2770-2014-127","type":"journal-article","created":{"date-parts":[[2014,5,20]],"date-time":"2014-05-20T17:11:39Z","timestamp":1400605899000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A one-dimensional prescribed curvature equation modeling the corneal shape"],"prefix":"10.1186","volume":"2014","author":[{"given":"Isabel","family":"Coelho","sequence":"first","affiliation":[]},{"given":"Chiara","family":"Corsato","sequence":"additional","affiliation":[]},{"given":"Pierpaolo","family":"Omari","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,5,20]]},"reference":[{"key":"736_CR1","doi-asserted-by":"publisher","first-page":"1498","DOI":"10.1016\/j.nonrwa.2011.11.014","volume":"13","author":"W Okrasi\u0144ski","year":"2012","unstructured":"Okrasi\u0144ski W, P\u0142ociniczak \u0141: A nonlinear mathematical model of the corneal shape. 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