The bifurcation of solutions in Banach spaces
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- by William S. Hall PDF
- Trans. Amer. Math. Soc. 161 (1971), 207-218 Request permission
Abstract:
Let $L:D \subset X \to D \subset {X^ \ast }$ be a densely defined linear map of a reflexive Banach space X to its conjugate ${X^\ast }$. Define M and ${M^\ast }$ to be the respective null spaces of L and its formal adjoint ${L^\ast }$. Let $f:X \to {X^\ast }$ be continuous. Under certain conditions on ${L^\ast }$ and f there exist weak solutions to $Lu = f(u)$ provided for each $w \in X,v(w) \in M$ can be found such that $f(v(w) + w)$ annihilates ${M^ \ast }$. Neither M and ${M^\ast }$ nor their annihilators need be the ranges of continuous linear projections. The results have applications to periodic solutions of partial differential equations.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 161 (1971), 207-218
- MSC: Primary 47.80
- DOI: https://doi.org/10.1090/S0002-9947-1971-0282267-2
- MathSciNet review: 0282267