Existence and uniqueness for a semilinear elliptic problem on Lipschitz domains in Riemannian manifolds II

Dindoš, Martin

doi:10.1090/S0002-9947-02-03210-5

Existence and uniqueness for a semilinear elliptic problem on Lipschitz domains in Riemannian manifolds II
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by Martin Dindoš PDF

Trans. Amer. Math. Soc. 355 (2003), 1365-1399 Request permission

Abstract:

Extending our recent work for the semilinear elliptic equation on Lipschitz domains, we study a general second-order Dirichlet problem $Lu-F(x,u)=0$ in $\Omega$. We improve our previous results by studying more general nonlinear terms $F(x,u)$ with polynomial (and in some cases exponential) growth in the variable $u$. We also study the case of nonnegative solutions.

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