{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:47:49Z","timestamp":1777448869878,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2010,10,1]],"date-time":"2010-10-01T00:00:00Z","timestamp":1285891200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2010,10]]},"abstract":"<jats:p>\n                    For many known examples of semilinear elliptic equations \u0394u+f(u)=0 in R\n                    <jats:sup>N<\/jats:sup>\n                    (N&gt;1), a bounded radial solution u(r) converges to a constant as r\u2192\u221e. Maier, in 1994, constructed, for N=2, an equation with a nonconvergent radial solution. Some necessary conditions for the existence of a nonconvergent solution were given by Maier, and later extended by Iaia. These conditions point out that, for N&gt;2, equations with nonconvergent solutions are rather rare.\n                  <\/jats:p>\n                  <jats:p>\n                    A nonconvergent solution must oscillate between two constant values c\n                    <jats:sub>1<\/jats:sub>\n                    &lt;c\n                    <jats:sub>2<\/jats:sub>\n                    and f must vanish at either c\n                    <jats:sub>1<\/jats:sub>\n                    or c\n                    <jats:sub>2<\/jats:sub>\n                    . In the neighborhood of one of these points, f must fluctuate wildly in an unusual way that excludes almost all common functions. In this paper, we give a further improvement of the above result with an alternative, simpler proof. The proof depends on an elementary, but nonobvious property of an initial value problem.\n                  <\/jats:p>","DOI":"10.3233\/asy-2010-0998","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:14:03Z","timestamp":1575054843000},"page":"1-11","source":"Crossref","is-referenced-by-count":1,"title":["Nonconvergent radial solutions of semilinear elliptic equations"],"prefix":"10.1177","volume":"70","author":[{"given":"Man Kam","family":"Kwong","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, SAR, China. E-mails: mankwong@polyu.edu.hk, mawhwong@inet.polyu.edu.hk"}]},{"given":"Solomon Wai-Him","family":"Wong","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, SAR, China. E-mails: mankwong@polyu.edu.hk, mawhwong@inet.polyu.edu.hk"}]}],"member":"179","published-online":{"date-parts":[[2010,10,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-0998","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2010-0998","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:13Z","timestamp":1777379953000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2010-0998"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2010,10]]}},"alternative-id":["10.3233\/ASY-2010-0998"],"URL":"https:\/\/doi.org\/10.3233\/asy-2010-0998","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10]]}}}