On the solvability in Hilbert space of certain nonlinear operator equations depending on parameters |
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Authors: | Athanassios G. Kartsatos Richard D. Mabry |
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Affiliation: | Department of Mathematics, University of South Florida, Tampa, Florida 33620 U.S.A. |
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Abstract: | The equation (*) Au − λTu + μCu = f is studied in a real separable Hilbert space H. Here, λ, μ > 0 are fixed constants and f ε H is fixed. The operators A: D H → H, C: D H → H are monotone and compact, respectively, where D denotes a closed ball in H. The operator T: H → H is linear, compact, self-adjoint and positive-definite. Degree-theoretic arguments are used for the existence of solutions of (*) and extensions of recent results of Kesavan are established. For example, it is shown, under additional assumptions, that there exists a constant μ0 > 0 such that (*) is solvable for all μ μ0 and all λ ε R. |
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