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On An Operator Equation Involving Mappings of Monotone Type

Chaitan P. Gupta
Proceedings of the American Mathematical Society
Vol. 53, No. 1 (Nov., 1975), pp. 143-148
DOI: 10.2307/2040386
Stable URL: http://www.jstor.org/stable/2040386
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On An Operator Equation Involving Mappings of Monotone Type
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Abstract

Let X be a real reflexive Banach space and A: X → 2X* a maximal monotone mapping such that the graph G(A) of A is weakly-closed in X × X* and 0 ε A(0). Also, let T: X → 2X* be a quasi-bounded coercive mapping of type (M) such that the effective domain D(T) of T contains a dense linear subspace X0 of X. Then it is shown that for each ω ε X* there exists a u ε X such that ω ε Au + Tu and the subset {u ε X ∣ ω ε Au + Tu} is a weakly-compact subset of X. An application to an elliptic nonlinear boundary value problem of Neumann type is given.

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