# Generalized Solutions of Functional Differential Inclusions

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The maximum principles present one of the classical parts in the qualitative theory of ordinary and partial differential equations. Although assertions about the maximum principles for functional differential equations can be interpreted in a corresponding sense as analogs of corresponding...

- On constant sign solutions (nonpositive) of certain functional differential inequality. Opluštil, Zdeněk // AIP Conference Proceedings;5/6/2009, Vol. 1124 Issue 1, p274
New sufficient conditions are found guaranteeing that every solution to the problem

uâ€²(t)>=l(u)(t), u(a)>=h(u) is nonpositive, where l:C([a,b];R)â†’L([a,b];R) is a linear bounded operator and h:C([a,b];R)â†’R is a linear bounded functional. Obtained results... - A survey and some new results on the existence of solutions of IPBVPS for first order functional differential equations. Liu, Yuji // Applications of Mathematics;Dec2009, Vol. 54 Issue 6, p527
This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhinâ€™s continuation theorem. Examples are presented...

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This paper is concerned with the existence and approximation of solutions for second order impulsive functional differential equations with boundary value conditions by monotone iterative technique. Sufficient conditions are obtained for the existence of extremal solutions.

- Periodic Boundary Value Problems for Second-Order Functional Differential Equations. Xiangling Fu; Weibing Wang // Journal of Inequalities & Applications;2010, Vol. 2010, p1
This note considers a periodic boundary value problem for a second-order functional differential equation. We extend the concept of lower and upper solutions and obtain the existence of extreme solutions by using upper and lower solution method.

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We establish certain sufficient conditions guaranteeing the boundedness of all solutions of some third-order delay differential equations.

- Asymptotic expansion of the solution of the initial value problem for a singularly perturbed ordinary differential equation. Khachay, O. // Differential Equations;Feb2008, Vol. 44 Issue 2, p282
We consider the Cauchy problem for the nonlinear differential equation where É› > 0 is a small parameter, f( x, u) âˆˆ C âˆž ([0, d] Ã— â„), R 0 > 0, and the following conditions are satisfied: f( x, u) = x âˆ’ u p + O( x 2 + | xu| + | u| p+1) as x, u â†’ 0, where p...

- Generalized Solutions of Functional Differential Inclusions with a Volterra Multi-Valued Mapping. Machina, Anna; Bulgakov, Aleksander // AIP Conference Proceedings;9/6/2007, Vol. 936 Issue 1, p356
We consider the initial value problem for a functional differential inclusion with a Volterra multi-valued mapping that is not necessarily decomposable in L1n[a,b]. In this case the methods known for multi-valued mappings cannot even be applied to the solvability problem of the perturbed...

- AN EIGENVALUE PROBLEM INVOLVING A FUNCTIONAL DIFFERENTIAL EQUATION ARISING IN A CELL GROWTH MODEL. VAN BRUNT, BRUCE; VLIEG-HULSTMAN, M. // ANZIAM Journal;04/01/2010, Vol. 51 Issue 4, p383
We interpret a boundary-value problem arising in a cell growth model as a singular Sturmâ€“Liouville problem that involves a functional differential equation of the pantograph type. We show that the probability density function of the cell growth model corresponds to the first eigenvalue...