On The Existence of Multiple Solutions of a Class of Third-Order Nonlinear Two-Point Boundary Value Problems
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A general approach is presented for proving existence of multiple solutions of the third-order nonlinear differential equation$$Au^{\prime\prime\prime}(x) + u^{\prime\prime}(x)u^\prime(x) + u^\prime(x)f(u(x))=0,\quad x \in [0,1] ,$$subject to given proper boundary conditions. The proof is constructive in nature, and could be used for numerical generation of the solution or closed-form analytical solution by introducing some special functions. The only restriction is about f(u), where it is supposed to be differentiable function with continuous derivative. It is proved the problem may admit no solution, may admit unique solution or may admit multiple solutions.KeywordsClosed-form solutionexact analytical solutionspecial functionunique solutionmultiple solutionsMathematics Subject Classification34B1535G3035G60References1.Shuicai L., Liao S.: An analytic approach to solve multiple solutions of a strongly nonlinear problem. Appl. Math. 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Prentice-Hall, Englewood Cliffs (1961)MATHGoogle ScholarCopyright information© Springer Basel 2015Authors and AffiliationsElyas Shivanian1Email authorFatemeh Abdolrazaghi11.Department of MathematicsImam Khomeini International UniversityQazvinIran About this article CrossMark Print ISSN 1660-5446 Online ISSN 1660-5454 Publisher Name Springer International Publishing About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s00009-015-0627-y_On The Existence of Multiple Solut", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s00009-015-0627-y_On The Existence of Multiple Solut", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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