论文信息 - Continuous nonlinear perturbations of linear accretive operators in banach spaces

Continuous nonlinear perturbations of linear accretive operators in banach spaces

Let A be a linear, closed, densely defined m-accretive operator from a Banach space X to itself, and let T(t), t ⩾ 0, be the semigroup of operators which has −A as its infinitesimal generator. Let B be a nonlinear, continuous, everywhere defined accretive operator from X to itself, and let S(t), t ⩾ 0, be the semigroup of nonlinear operators which has −B as its infinitesimal generator. It is shown that for all x ϵ X, t ⩾ 0, limn → ∞(T(tn) S(tn))nx = U(t)x exists, U(t)x = T(t)x − ∝0t T(t − s) BU(s) x ds, and U(t), t ⩾ 0, is a strongly continuous semigroup of nonlinear contractions on X. It is shown also that −(A + B) is the infinitesimal generator of U(t), t ⩾ 0, and A + B is m-accretive on X.

Glenn F. Webb | G. Webb

[1] F. Browder. Nonlinear accretive operators in Banach spaces , 1967 .

[2] Amnon Pazy,et al. Semi-groups of nonlinear contractions and dissipative sets☆ , 1969 .

[3] H. Brezis,et al. Semigroups of nonlinear contractions on convex sets , 1970 .

[4] H. Trotter. On the product of semi-groups of operators , 1959 .

[5] Michael G. Crandall,et al. GENERATION OF SEMI-GROUPS OF NONLINEAR TRANSFORMATIONS ON GENERAL BANACH SPACES, , 1971 .

[6] Tosio Kato. Perturbation theory for linear operators , 1966 .

[7] R. Martin,et al. A global existence theorem for autonomous differential equations in a Banach space , 1970 .

[8] J. Neuberger. An exponential formula for one-parameter semi-groups of nonlinear transformations , 1966 .

[9] I. Segal. Non-Linear Semi-Groups , 1963 .

[10] Felix E. Browder,et al. Nonlinear equations of evolution and nonlinear accretive operators in Banach spaces , 1967 .

[11] The logarithmic derivative and equations of evolution in a Banach space , 1970 .

[12] G. Webb. Nonlinear evolution equations and product integration in Banach spaces. , 1970 .

[13] Shinnosuke Oharu,et al. APPROXIMATION OF SEMI-GROUPS OF NONLINEAR OPERATORS , 1970 .

[14] Haim Brezis,et al. Perturbations of nonlinear maximal monotone sets in banach space , 1970 .