Transactions of the American Mathematical Society

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

Author(s): Martin Dindos
Journal: Trans. Amer. Math. Soc. 355 (2003), 1365-1399.
MSC (2000): Primary 35J65, 35B65; Secondary 46E35, 42B20
Posted: December 2, 2002
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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

in $\Omega$ . We improve our previous results by studying more general nonlinear terms

with polynomial (and in some cases exponential) growth in the variable

. We also study the case of nonnegative solutions.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35J65, 35B65, 46E35, 42B20

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

DOI: 10.1090/S0002-9947-02-03210-5
PII: S 0002-9947(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
Posted: December 2, 2002
Copyright of article: Copyright 2002, American Mathematical Society

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