Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10427111 | Nonlinear Analysis: Theory, Methods & Applications | 2005 | 7 Pages |
Abstract
We consider the boundary value problem with the Dirichlet condition in a Banach space for a semilinear elliptic equation on a bounded domain in Rn whose nonlinear term satisfies the Lipschitz condition. If the Lipschitz constant L is less than λ1, then this problem has a unique solution, where λ1 is the least eigenvalue of the corresponding (real valued) eigenvalue problem. On the other hand, for any L>λ1 we can construct a nonlinear term with the Lipschitz constant L such that the solution set is homeomorphic to any prescribed closed subset of the Banach space.
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Authors
Tokushi Sato, Eiji Yanagida,