{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,30]],"date-time":"2025-09-30T00:10:30Z","timestamp":1759191030783},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,6,1]],"date-time":"2014-06-01T00:00:00Z","timestamp":1401580800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2015,3]]},"DOI":"10.1007\/s10915-014-9871-8","type":"journal-article","created":{"date-parts":[[2014,5,31]],"date-time":"2014-05-31T19:31:38Z","timestamp":1401564698000},"page":"652-673","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Convergence Analysis of a Minimax Method for Finding Multiple Solutions of Semilinear Elliptic Equation: Part I\u2014On Polyhedral Domain"],"prefix":"10.1007","volume":"62","author":[{"given":"Xudong","family":"Yao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,6,1]]},"reference":[{"key":"9871_CR1","volume-title":"Sobolev Spaces","author":"Robert Alexander Adams","year":"2003","unstructured":"Adams, Robert Alexander, Fournier, John J.F.: Sobolev Spaces. Academic Press, New York (2003)"},{"key":"9871_CR2","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/0022-1236(73)90051-7","volume":"14","author":"A Ambrosetti","year":"1973","unstructured":"Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349\u2013381 (1973)","journal-title":"J. Funct. Anal."},{"key":"9871_CR3","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1002\/cpa.3160440808","volume":"44","author":"H Brezis","year":"1991","unstructured":"Brezis, H., Nirenberg, L.: Remarks on finding critical points. Commun. Pure Appl. Math. 44, 939\u2013963 (1991)","journal-title":"Commun. Pure Appl. Math."},{"key":"9871_CR4","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1016\/j.physd.2010.01.017","volume":"239","author":"X Chen","year":"2010","unstructured":"Chen, X., Lin, T.C., Wei, J.C.: Blowup and solitary wave solutions with ring profiles of two-component nonlinear Schrodinger systems. Physica D 239, 613\u2013626 (2010)","journal-title":"Physica D"},{"key":"9871_CR5","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1090\/S0025-5718-10-02336-7","volume":"79","author":"X Chen","year":"2010","unstructured":"Chen, X., Zhou, J.: A local min-max-orthogonal method for finding multiple solutions to noncooperative elliptic systems. Math. Comput. 79, 2213\u20132236 (2010)","journal-title":"Math. Comput."},{"key":"9871_CR6","doi-asserted-by":"crossref","first-page":"1614","DOI":"10.1016\/j.apnum.2007.09.007","volume":"58","author":"X Chen","year":"2008","unstructured":"Chen, X., Zhou, J., Yao, X.: A numerical method for finding multiple co-existing solutions to nonlinear cooperative systems. Appl. Numer. Math. 58, 1614\u20131627 (2008)","journal-title":"Appl. Numer. Math."},{"key":"9871_CR7","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/0362-546X(93)90147-K","volume":"20","author":"YS Choi","year":"1993","unstructured":"Choi, Y.S., McKenna, P.J.: A mountain pass method for the numerical solution of semilinear elliptic problems. Nonlinear Anal. 20, 417\u2013437 (1993)","journal-title":"Nonlinear Anal."},{"key":"9871_CR8","unstructured":"Ciarlet, P.G., Lions, J.L.: Handbook of Numerical Analysis. Elsevier Science Publishers B. V, North-Holland (1975)"},{"key":"9871_CR9","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0362-546X(98)00086-8","volume":"38","author":"Z Ding","year":"1999","unstructured":"Ding, Z., Costa, D., Chen, G.: A high linking method for sign changing solutions for semilinear elliptic equations. Nonlinear Anal. 38, 151\u2013172 (1999)","journal-title":"Nonlinear Anal."},{"key":"9871_CR10","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1007\/s10915-013-9689-9","volume":"56","author":"A Le","year":"2013","unstructured":"Le, A., Wang, Z.Q., Zhou, J.: Finding multiple solutions to elliptic PDE with nonlinear boundary conditions. J. Sci. Comput. 56, 591\u2013615 (2013)","journal-title":"J. Sci. Comput."},{"key":"9871_CR11","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1137\/S1064827599365641","volume":"23","author":"Y Li","year":"2001","unstructured":"Li, Y., Zhou, J.: A minimax method for finding multiple critical points and its applications to nonlinear PDEs. SIAM J. Sci. Comput. 23, 840\u2013865 (2001)","journal-title":"SIAM J. Sci. Comput."},{"key":"9871_CR12","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1137\/S1064827500379732","volume":"24","author":"Y Li","year":"2002","unstructured":"Li, Y., Zhou, J.: Convergence results of a local minimax method for finding multiple critical points. SIAM J. Sci. Comput. 24, 865\u2013885 (2002)","journal-title":"SIAM J. Sci. Comput."},{"key":"9871_CR13","unstructured":"Ni, W.M.: Some aspects of semilinear elliptic equations. Dept. of Math. National Tsing Hua Univ., Hsinchu, Taiwan, Rep. of China (1987)"},{"key":"9871_CR14","doi-asserted-by":"crossref","unstructured":"Rabinowitz, P.: Minimax Method in Critical Point Theory with Application to Differential Equations, CBMS Regional Conference Series in Mathematics, No. 65, AMS, Providence (1986)","DOI":"10.1090\/cbms\/065"},{"key":"9871_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03212-1","volume-title":"Variational Methods","author":"M Struwe","year":"1996","unstructured":"Struwe, M.: Variational Methods. Springer, New York (1996)"},{"key":"9871_CR16","first-page":"1778","volume":"29","author":"C Wang","year":"2013","unstructured":"Wang, C., Zhou, J.: An orthogonal subspace minimization method for finding multiple solutions to defocusing Schrodinger equation with symmetries. NMPDE 29, 1778\u20131800 (2013)","journal-title":"NMPDE"},{"key":"9871_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4146-1","volume-title":"Minimax Theorems","author":"M Willem","year":"1996","unstructured":"Willem, M.: Minimax Theorems. Birkh\u00e4user, Boston (1996)"},{"key":"9871_CR18","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1137\/100810411","volume":"34","author":"ZQ Xie","year":"2012","unstructured":"Xie, Z.Q., Yuan, Y.J., Zhou, J.: On finding multiple solutions to a singularly perturbed Neumann problem. SIAM J. Sci. Comput. 34, 395\u2013420 (2012)","journal-title":"SIAM J. Sci. Comput."},{"key":"9871_CR19","doi-asserted-by":"crossref","first-page":"2087","DOI":"10.1090\/S0025-5718-2013-02669-5","volume":"82","author":"X Yao","year":"2013","unstructured":"Yao, X.: A minimax method for finding saddle critical points of upper semi-differentiable locally Lipschitz continuous functional in Banach space and its convergence. Math. Comput. 82, 2087\u20132136 (2013)","journal-title":"Math. Comput."},{"key":"9871_CR20","doi-asserted-by":"crossref","first-page":"1796","DOI":"10.1137\/S1064827503430503","volume":"26","author":"X Yao","year":"2005","unstructured":"Yao, X., Zhou, J.: A minimax method for finding multiple critical points in Banach spaces and its application to quasi-linear elliptic PDE. SIAM J. Sci. Comput. 26, 1796\u20131809 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"9871_CR21","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1137\/050627320","volume":"45","author":"X Yao","year":"2007","unstructured":"Yao, X., Zhou, J.: Unified convergence results on a minimax algorithm for finding multiple critical points in Banach spaces. SIAM J. Num. Anal. 45, 1330\u20131347 (2007)","journal-title":"SIAM J. Num. Anal."},{"key":"9871_CR22","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1137\/060651859","volume":"29","author":"X Yao","year":"2007","unstructured":"Yao, X., Zhou, J.: Numerical methods for computing nonlinear eigenpairs: Part I. Isohomogeneous cases. SIAM J. Sci. Comput. 29, 1355\u20131374 (2007)","journal-title":"SIAM J. Sci. Comput."},{"key":"9871_CR23","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1137\/060656425","volume":"30","author":"X Yao","year":"2008","unstructured":"Yao, X., Zhou, J.: Numerical methods for computing nonlinear eigenpairs: Part II. Non-Isohomogeneous cases. SIAM J. Sci. Comput. 30, 937\u2013956 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"9871_CR24","doi-asserted-by":"crossref","unstructured":"Yao, X., Zhou, J.: A local minimax characterization for computing multiple nonsmooth saddle critical points, Ser. B. Math. Program. 104(2\u20133), 749\u2013760 (2005)","DOI":"10.1007\/s10107-005-0636-x"},{"key":"9871_CR25","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1080\/01630563.2011.597630","volume":"32","author":"J Zhou","year":"2011","unstructured":"Zhou, J.: Global sequence convergence of a local minimax method for finding multiple solutions in Banach spaces. Num. Funct. Anal. Optim. 32, 1365\u20131380 (2011)","journal-title":"Num. Funct. Anal. Optim."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-014-9871-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-014-9871-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-014-9871-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T08:45:47Z","timestamp":1559465147000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-014-9871-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,1]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,3]]}},"alternative-id":["9871"],"URL":"https:\/\/doi.org\/10.1007\/s10915-014-9871-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,1]]}}}