{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T01:05:54Z","timestamp":1775091954231,"version":"3.50.1"},"reference-count":21,"publisher":"World Scientific Pub Co Pte Ltd","issue":"15","funder":[{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2018A030313536"],"award-info":[{"award-number":["2018A030313536"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,12,15]]},"abstract":"<jats:p> In this paper, a mathematical model for solid vascular tumor growth with Gibbs\u2013Thomson relation is studied. On the free boundary, we consider Gibbs\u2013Thomson relation which means energy is expended to maintain the tumor structure. Supposing that the nutrient is the source of the energy, the nutrient denoted by [Formula: see text] satisfies [Formula: see text] where [Formula: see text] is a constant representing the ability of the tumor to absorb the nutrient through its blood vessels; [Formula: see text] is concentration of the nutrient outside the tumor; [Formula: see text] is the mean curvature; [Formula: see text] denotes adhesiveness between cells and [Formula: see text] denotes the exterior normal derivative on [Formula: see text] The existence, uniqueness and nonexistence of radially symmetric solutions are discussed. By using the bifurcation method, we discuss the existence of nonradially symmetric solutions. The results show that infinitely many nonradially symmetric solutions bifurcate from the radially symmetric solutions. <\/jats:p>","DOI":"10.1142\/s0218127421502321","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T11:30:05Z","timestamp":1638876605000},"source":"Crossref","is-referenced-by-count":1,"title":["Bifurcation of a Mathematical Model for Tumor Growth with Angiogenesis and Gibbs\u2013Thomson Relation"],"prefix":"10.1142","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1961-3398","authenticated-orcid":false,"given":"Shihe","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong 526061, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meng","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong 526061, P. R. 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