{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:03:27Z","timestamp":1773792207988,"version":"3.50.1"},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,6,6]],"date-time":"2011-06-06T00:00:00Z","timestamp":1307318400000},"content-version":"vor","delay-in-days":10748,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math Methods in App Sciences"],"published-print":{"date-parts":[[1982,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider the existence of a nontrivial solution of the following equation:<jats:disp-formula\/>where<jats:italic>g<\/jats:italic>is a nondecreasing function defined on R<jats:sup>1<\/jats:sup>, satisfies<jats:italic>g<\/jats:italic>(O) = O, and some other additional conditions.<\/jats:p><jats:p>Our results and methods are quite similar to those associated with recent work on the nonlinear wave equation [1]\u2010[8]:<jats:disp-formula\/>.<\/jats:p>","DOI":"10.1002\/mma.1670040113","type":"journal-article","created":{"date-parts":[[2007,3,29]],"date-time":"2007-03-29T20:48:06Z","timestamp":1175201286000},"page":"194-205","source":"Crossref","is-referenced-by-count":23,"title":["Nontrivial periodic solutions of a nonlinear beam equation"],"prefix":"10.1002","volume":"4","author":[{"given":"K. C.","family":"Chang","sequence":"first","affiliation":[]},{"given":"Luis","family":"Sanchez","sequence":"additional","affiliation":[]},{"given":"P.","family":"Rabinowitz","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,6,6]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"539","article-title":"Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations","volume":"4","author":"Amann H.","year":"1980","journal-title":"Annal. Sc. norm. Sup. Pisa"},{"key":"e_1_2_1_3_2","volume-title":"Th\u00e8se de 3 \u00e8me cycle","author":"Bahri A.","year":"1979"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"Br\u00e9zis H. Coron J. M. Nirenberg L.:Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz Comm. Pure Appl. Math.1980","DOI":"10.1002\/cpa.3160330507"},{"key":"e_1_2_1_5_2","article-title":"A new proof and an extension of a theorem of P","volume":"2158","author":"Chang K. C.","year":"1980","journal-title":"Rabinowitz. MRC Report"},{"key":"e_1_2_1_6_2","article-title":"Multiple periodic solutions for the asymptotically linear wave equation","volume":"2179","author":"Chang K. C.","year":"1980","journal-title":"MRC Report"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1002\/cpa.3160310103","article-title":"Free vibrations for a semilinear wave equation","volume":"30","author":"Rabinowitz P.","year":"1978","journal-title":"Comm. Pure Appl. Math."},{"key":"e_1_2_1_8_2","first-page":"305","article-title":"Solutions p\u00e9riodiques non triviales d'une \u00e9quation d'\u00e9volution non lin\u00e9aire du quatri\u00e8me ordre","volume":"290","author":"Sanchez L.","year":"1980","journal-title":"C. R. A. S. Paris"},{"key":"e_1_2_1_9_2","unstructured":"Sanchez L.:Solu\u00e7\u00f5es peri\u00f3dicas de certas equa\u00e7\u00f5es diferenciais n\u00e3o lineares. Thesis Faculdade de Ci\u011bncias de Lisboa 1980"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(73)90051-7"}],"container-title":["Mathematical Methods in the Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmma.1670040113","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/mma.1670040113","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,12]],"date-time":"2024-02-12T13:12:11Z","timestamp":1707743531000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/mma.1670040113"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,1]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1982,1]]}},"alternative-id":["10.1002\/mma.1670040113"],"URL":"https:\/\/doi.org\/10.1002\/mma.1670040113","archive":["Portico"],"relation":{},"ISSN":["0170-4214","1099-1476"],"issn-type":[{"value":"0170-4214","type":"print"},{"value":"1099-1476","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,1]]}}}