Browsing College of Engineering and Science by Author "Lakshmikantham, V."
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Existence Criteria for Singular Initial Value Problems with Sign Changing Nonlinearities
Agarwal, Ravi P.; O’Regan, Donal; Lakshmikantham, V. (2001)A general existence theory is presented for initial value problems where our nonlinearity may be singular in its dependent variable and may also change sign. -
Generalized flow invariance for differential inclusions
Bhaskar, Tarun Gnana; Lakshmikantham, V. (2005-05-12)We introduce a generalized notion of invariance for differential inclusions, using a proximal aiming condition in terms of proximal normals. A set of sufficient conditions for the weak and strong invariance in the generalized ... -
Monotone iterations for differential equations with a parameter
Jankowski, Tadeusz; Lakshmikantham, V. (1997)Consider the problem {y′(t)=f(t,y(t),λ),t∈J=[0,b],y(0)=k0,G(y,λ)=0. Employing the method of upper and lower solutions and the monotone iterative technique, existence of extremal solutions for the above equation are proved. -
On Solvability of Mixed Monotone Operator Equations with Applications to Mixed Quasimonotone Differential Systems Involving Discontinuities
Heikkilä, Seppo V.; Kumpulainen, Martti; Lakshmikantham, V. (1992)In this paper we shall first study solvability of mixed monotone systems of operator equations in an ordered normed space by using a generalized iteration method. The obtained results are then applied to prove existence ... -
Stability of Conditionally Invariant Sets and Controlled Uncertain Dynamic Systems on Time Scales
Lakshmikantham, V.; Drici, Zahia (1995)A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected ... -
Variational Lyapunov method and stability theory
Lakshmikantham, V.; Liu, Xinzhi; Leela, S. G (1998)By unifying the method of variation of parameters and Lyapunov's second method, we develop a fruitful technique which we call variational Lyapunov method. We then consider the stability theory in this new framework showing ...