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


Author: Martin Dindos
Journal: Trans. Amer. Math. Soc. 355 (2003), 1365-1399
MSC (2000): Primary 35J65, 35B65; Secondary 46E35, 42B20
DOI: https://doi.org/10.1090/S0002-9947-02-03210-5
Published electronically: December 2, 2002
MathSciNet review: 1946396
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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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Additional Information

Martin Dindos
Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
Email: dindos@math.cornell.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03210-5
Keywords: Nonlinear equations, semilinear elliptic problems, Dirichlet boundary problems, Lipschitz domains, Riemannian manifolds
Received by editor(s): September 11, 2001
Received by editor(s) in revised form: July 24, 2002
Published electronically: December 2, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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