Article ID Journal Published Year Pages File Type
10427111 Nonlinear Analysis: Theory, Methods & Applications 2005 7 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Engineering Engineering (General)
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