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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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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Additional Information
  • Martin Dindoš
  • Affiliation: Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York 14853-4201
  • ORCID: 0000-0002-6886-7677
  • Email: dindos@math.cornell.edu
  • Received by editor(s): September 11, 2001
  • Received by editor(s) in revised form: July 24, 2002
  • Published electronically: December 2, 2002
  • © Copyright 2002 American Mathematical Society
  • 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
  • MathSciNet review: 1946396