Solvability of nonlinear equations in a cone of a banach space
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Abstract
The solvability conditions for the equation Tu+F(u)=0 are found in the case where the operator [T+F′(u)]−1 exists only for u∈K, where K is a cone in a Banach space X. An application concerning the solvability of boundary-value problems for systems of second-order differential equations is provided.
Keywords
Banach Space Solvability Condition Inverse Operator Real Banach Space Nonnegative Solution
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© Kluwer Academic/Plenum Publishers 2000