On the positive solutions of semilinear equations Δ𝑢+𝜆𝑢-ℎ𝑢^{𝑝}=0 on the compact manifolds

Ouyang, Tiancheng

doi:10.1090/S0002-9947-1992-1055810-7

On the positive solutions of semilinear equations $\Delta u+\lambda u-hu^ p=0$ on the compact manifolds
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Trans. Amer. Math. Soc. 331 (1992), 503-527 Request permission

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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