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作 者:廖芳芳 王炎超 Liao Fangfang;Wang Yanchao(School of Mathematics,Southeast University,Nanjing,Jiangsu 210096,China;Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China;College of Science,Hohai University,Nanjing,Jiangsu 210098,China)
机构地区:[1]东南大学数学学院,江苏南京210096 [2]上海师范大学数理学院,上海200234 [3]河海大学理学院,江苏南京210098
出 处:《上海师范大学学报(自然科学版)》2018年第3期349-355,共7页Journal of Shanghai Normal University(Natural Sciences)
基 金:The National Natural Science Foundation of China(11701375);The Natural Science Foundation of Shanghai Normal University(SK201709);The QingLan project of Jiangsu Province
摘 要:近些年,非线性代数方程或者非线性代数方程组非平凡解的存在性研究吸引了国内外一些学者的关注,也取得了一些很有意义的结果.应用经典的锥不动点定理,研究了一类非线性代数方程组正解的存在性问题,并用非线性项的渐进行为刻画了其特征区间.和已有文献比较,证明方法更简捷,并改进了已有的结果.During the last few years, the study on the existence of nontrivial solutions for nonlinear algebraic equations or nonlinear systems of algebraic equations has attracted much attention of some researchers, and some interesting results have been obtained. In this paper, we apply a well-known fixed point theorem to study the existence of positive solutions to a nonlinear system of algebraic equations. Moreover, the eigenvalue intervals are also characterized by using the behaviors of the nonlinear term at the origin and at the infinity. Compared to those in the literature, the methods used in this paper are much easier, and our new results generalize and improve those existed results.
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