Nonlinear differential equations in abstract spaces. (English) Zbl 0456.34002

Lakshmikantham, V.; Leela, S.

International Series in Nonlinear Mathematics: Theory, Methods and Applications, Vol. 2. Oxford etc.: Pergamon Press. X, 258 p. $ 45.00; £18.75 (1981).

MSC:

34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations
34G20	Nonlinear differential equations in abstract spaces
34B15	Nonlinear boundary value problems for ordinary differential equations
34D20	Stability of solutions to ordinary differential equations
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34C11	Growth and boundedness of solutions to ordinary differential equations
34E10	Perturbations, asymptotics of solutions to ordinary differential equations

Keywords:

book; nonlinear ordinary differential equations in Banach spaces; measures of noncompactness; Cauchy problem; compactness type conditions; dissipative type conditions; successive approximations; existence in closed sets; nonlinear semigroups; (m-) dissipative operators; difference approximations; integral solutions and limit solutions; global existence; differential inequalities in cones; quasilinearizations; asymptotic equilibrium; stability; asymptotic behavior; Lyapunov functions; weak (non-) compactness; equations with delay; boundary value problems; monotone iterative methods

Citations:

Zbl 0257.34002; Zbl 0333.47023; Zbl 0361.34050