{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:15:03Z","timestamp":1772291703587,"version":"3.50.1"},"reference-count":13,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,1,20]],"date-time":"2009-01-20T00:00:00Z","timestamp":1232409600000},"content-version":"unspecified","delay-in-days":5955,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proceedings of the Edinburgh Mathematical Society"],"published-print":{"date-parts":[[1992,10]]},"abstract":"<jats:p>We prove the existence of a solution <jats:italic>u<\/jats:italic>(.,.;\u03b1,\u03b2) of the Darboux problem <jats:italic>u<\/jats:italic><jats:sub>xy<\/jats:sub>\u2208<jats:italic>F<\/jats:italic>(<jats:italic>x<\/jats:italic>, <jats:italic>y<\/jats:italic>, <jats:italic>u<\/jats:italic>), <jats:italic>u<\/jats:italic>(<jats:italic>x<\/jats:italic>,0) = \u03b1(<jats:italic>x<\/jats:italic>), <jats:italic>u<\/jats:italic>(0, <jats:italic>y<\/jats:italic>) = \u03b2(<jats:italic>y<\/jats:italic>), which is continuous with respect to (\u03b1,\u03b2). We assume that <jats:italic>F<\/jats:italic> is Lipschitzean with respect to <jats:italic>u<\/jats:italic> but not necessarily convex valued.<\/jats:p>","DOI":"10.1017\/s0013091500005666","type":"journal-article","created":{"date-parts":[[2008,12,19]],"date-time":"2008-12-19T15:41:00Z","timestamp":1229701260000},"page":"375-382","source":"Crossref","is-referenced-by-count":9,"title":["On a non-convex hyperbolic differential inclusion"],"prefix":"10.1017","volume":"35","author":[{"given":"Vasile","family":"Staicu","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,1,20]]},"reference":[{"key":"S0013091500005666_ref009","first-page":"149","article-title":"Integrals, conditions expectations and martingales of multivalued functions","volume":"1","author":"Hiai","year":"1971","journal-title":"J. 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Ekvac."},{"key":"S0013091500005666_ref012","first-page":"41","article-title":"Sur le problem de Darboux pour l'equation \u22022z\/\u2202x\u2202y\u2208F(x, y, z)","volume":"32","author":"Teodoru","year":"1986","journal-title":"An. Stiint. Univ. \u201cAl. I. Cuza\u201d lasi Sect. I a Mat."},{"key":"S0013091500005666_ref007","doi-asserted-by":"publisher","DOI":"10.1137\/0305040"},{"key":"S0013091500005666_ref010","first-page":"281","article-title":"Generalized solutions of partial differential inclusions depending on a parameter","volume":"107","author":"Marano","year":"1989","journal-title":"Rend. Acad. Naz. Sci. XL Mem. Mat."},{"key":"S0013091500005666_ref013","first-page":"281","article-title":"Continuous selections for multifunctions satisfying Carath\u00e9odory type conditions. The Darboux problem associated to a multivalued equation","volume":"6","author":"Teodoru","year":"1987","journal-title":"Proc. Itinerant Seminar on Functional Equations, Approximation and Convexity"},{"key":"S0013091500005666_ref011","first-page":"173","article-title":"Le problem de Darboux pour une equation aux derivees partielles multivoque","volume":"31","author":"Teodoru","year":"1985","journal-title":"An. Stiint. Univ. \u201cAl. I. Cuza\u201d lasi Sect. I a Mat."},{"key":"S0013091500005666_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69512-4"},{"key":"S0013091500005666_ref008","doi-asserted-by":"publisher","DOI":"10.4064\/sm-76-2-163-174"}],"container-title":["Proceedings of the Edinburgh Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0013091500005666","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T20:33:01Z","timestamp":1558038781000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0013091500005666\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,10]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,10]]}},"alternative-id":["S0013091500005666"],"URL":"https:\/\/doi.org\/10.1017\/s0013091500005666","relation":{},"ISSN":["0013-0915","1464-3839"],"issn-type":[{"value":"0013-0915","type":"print"},{"value":"1464-3839","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,10]]}}}