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- W2809067872 abstract "Let E be a real reflexive Banach space, E∗ be the dual space of E and (T: D(T)subseteq Eto 2^{E^{*}}), (S:D(S)subseteq Eto 2^{E^*}) be two maximal monotone operators such that D(T) ∩ D(S) ≠ ∅. Assume that there exist x0 ∈ E, r > 0, λ0 > 0 such that inff ∈ Tx(f, x − x0) is lower bounded on each bounded subset of D(T) and, if, for each y ∈ B(x0, r), g ∈ E∗, x n ∈ D(T) and λ n ∈ (0, λ0) with (gin Tx_n+ S_{lambda _n}x_n+Jx_n) for each n = 1, 2, ⋯, ({R_{lambda _n}^Sx_n}_{=1}^{infty }) is bounded, then we have $$displaystyle inf _{ngeq 1}(S_{lambda _n}x_n,R_{lambda _n}^Sx_n-y)>-infty , $$where (R_{lambda }^S) is the Yosida resolvent of S, then T + S is maximal monotone. Also, we construct a degree theory for the sum of two maximal monotone operators, where the sum may not be maximal monotone, and the degree theory is also applied to study the operator equation 0 ∈ (T + S)x. Finally, we give some applications of the main results to nonlinear partial differential equations." @default.
- W2809067872 created "2018-06-29" @default.
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- W2809067872 date "2018-01-01" @default.
- W2809067872 modified "2023-09-24" @default.
- W2809067872 title "On the Maximality of the Sum of Two Maximal Monotone Operators" @default.
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- W2809067872 doi "https://doi.org/10.1007/978-3-319-89800-1_3" @default.
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