Positive solutions of semilinear elliptic eigenvalue problems with concave nonlinearities
Positive solutions of semilinear elliptic eigenvalue problems with concave nonlinearities
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DOI：
10.57262/ade/1355867408
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发表时间：
2007-01
影响因子：
1.4
通讯作者：
K. Umezu
中科院分区：
文献类型：
--
作者：
K. Umezu
抽象。本文证明了在光滑有界区域内和边界上具有凹非线性项的半线性椭圆型边值问题正解的存在性和不存在性。我们的方法依赖于子和上解，以及可能包含与边值问题相关的能量泛函的临界点的Nehari流形。这种方法有助于我们研究Nehari流形的性质。
Abstract. In this paper, we prove the existence and nonexistence results for positive solutions to semilinear elliptic boundary value problems, with concave nonlinearities inside a smooth bounded domain and on the boundary. Our approach relies on sub and supersolutions, as well as the Nehari manifold that may contain the critical points for the energy functional associated with the boundary value problem. The fibering method helps us to study the properties of the Nehari manifold.