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具梯度项的次线性椭圆型方程解的分析

Discussion of Solution of Sublinear Elliptic Equations with Gradient Term
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摘要 本文研究了1类具梯度项的次线性椭圆型方程大解和完全有界解的存在性问题。运用上下解方法和极值原理分别得到了Rn上方程存在完全大解的充分必要条件和存在完全有界解的充分条件,并且证明了该方程在Rn中光滑有界区域Ω上不存在大解。 The existence of large solutions and entire bounded solutions for a class of sublinear elliptic equations with gradient term is discussed in this paper.By using the method of super-subsolutions and maximum principle,the authors obtain the necessary and sufficient conditions for the existence of entire large solutions of the equation and the sufficient conditions for the existence of entire bounded solutions of the equation in Rn respectively.Finally,the nonexistence of large solutions of the equation in a bounded domain Ω with smooth boundary in Rn is proved.
作者 杨春娜 王建
机构地区 中国海洋大学数学科学学院
出处 《中国海洋大学学报（自然科学版）》 CAS CSCD 北大核心 2011年第7期197-201,共5页 Periodical of Ocean University of China
基金 国家自然科学基金项目(10371050) 中央高校基本科研业务费青年教师专项基金项目(841113017)资助
关键词 次线性椭圆型方程 梯度项 大解 完全有界解 上下解方法 极值原理 sublinear elliptic equation gradient term entire large solutions entire bounded solutions super-subsolutions maximum principle
分类号 O175.25 [理学—基础数学]
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参考文献11

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中国海洋大学学报（自然科学版）
2011年 第7期

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