Positive solutions of sublinear elliptic boundary value problems
Positive solutions of sublinear elliptic boundary value problems
复制标题
次线性椭圆边值问题的正解
DOI：
10.1016/s0362-546x(96)00059-4
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
K. Umezu
中科院分区：
文献类型：
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作者：
Kazuaki Taira;K. Umezu
本文是Taira-Umezu [TU 1]和[TU 2]的继续，其中我们研究了一类非线性二阶椭圆型微分算子退化边值问题的全局静态分歧理论.以往的文献利用Leray-Schauder度理论讨论了渐近线性和非线性的情形，例如非线性项u+ 1/u和up，p> 1，在u=+∞附近.本文的目的是研究更一般的非线性项，如log（1+ u）和e-u，并利用上下解方法证明非线性椭圆边值问题正解的存在唯一性.我们注意到，由于边界条件是退化的，变分法将失效。设D是欧氏空间RN的有界区域，N≥ 2，C∞边界<$D，其闭包D= D <$<$D是N维紧C∞有边界流形.我们让
This paper is a continuation of the previous papers Taira-Umezu [TU1] and [TU2] where we studied global static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The previous papers treated the asymptotic linear and nonlinear cases, for example, such nonlinear terms as u+ 1/u and up, p> 1, near u=+∞, by using the Leray-Schauder degree theory. The purpose of this paper is to study more general nonlinear terms such as√ u, log (1+ u) and e− u, and is to prove the existence and uniqueness of positive solutions of nonlinear elliptic boundary value problems, by making good use of the super-subsolution method. We remark that the variational method would break down, since our boundary condition is degenerate. Let D be a bounded domain of Euclidean space RN, N≥ 2, with C∞ boundary∂ D; its closure D= D∪∂ D is an N-dimensional, compact C∞ manifold with boundary. We let