Transactions of the American Mathematical Society

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On the positive solutions of semilinear equations $ \Delta u+\lambda u-hu\sp p=0$ on the compact manifolds


Author: Tiancheng Ouyang
Journal: Trans. Amer. Math. Soc. 331 (1992), 503-527
MSC: Primary 35B05; Secondary 35J60, 58G20, 58G30
MathSciNet review: 1055810
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Abstract: In this paper, we study the existence, nonexistence, and uniqueness of positive solutions of semilinear equations $ \Delta u + \lambda u - h{u^p}= 0$ on compact Riemannian manifolds as well as on bounded smooth domains in $ {R^n}$ with homogeneous Dirichlet or Neumann boundary conditions.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1055810-7
Article copyright: © Copyright 1992 American Mathematical Society