Results 181 to 190 of about 1,565 (208)

Impulsive Boundary Value Problems for First-order Ordinary Differential Inclusions

Acta Mathematicae Applicatae Sinica, 2007
The authors prove existence results for the following class of boundary value problems \[ u'(t)+\lambda(t)u(t)\in F(t,u(t)), \quad\text{a. e. }t\in [0,T]\backslash \{t_{1},t_{2},\ldots,t_{m}\}, \] \[ \Delta u| _{t=t_{k}}=I_{k}(u(t_{k}^{-})), \quad k=1,2,\ldots,m, \] \[ u(0)-u(T)=\mu, \] where \(F:[0,T]\times\mathbb R^{n}\to P(\mathbb R^{n})\) is a ...
Liu, Yi-Cheng, Wu, Jun, Li, Zhi-Xiang
exaly   +2 more sources

Ordinary Differential Inclusions with Internal and External Perturbations

Differential Equations, 2000
Let \(\mathbb{R}^ n\) be the space of column \(n\)-vectors with Euclidean norm \(|\cdot|\); \(\text{comp}[\mathbb{R}^ n]\) be the set of all non-empty bounded closed subsets of \(\mathbb{R}^ n\); \(B[u,r]\) be the closed ball with center \(u\) and radius \(r>0\). For \(V\subset \mathbb{R}^ n,\) \(\operatorname {co}V\) denote the convex hull of the set \
Bulgakov, A. I., Efremov, A. A., Panasenko, E. A.   +2 more
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Connection of the solution of a stochastic differential inclusion with the solution of an ordinary differential equation

Journal of Soviet Mathematics, 1993
Consider the stochastic differential inclusion \[ (1)\quad du(t)+A(t,u(t))dt+C(u(t))dt+B(t,u(t))dw(t)\ni 0,\quad u(0)=u_ 0, \] where A,B: [0,T]\(\times R\to R\), and C is a maximal monotone set-valued map from R into R. Under some regularity conditions, the author associates with this inclusion the family of ordinary differential equations \[ (2)\quad ...
openaire   +3 more sources

On the iterative inclusion of solutions in initial-value problems for ordinary differential equations

Computing, 1979
This note contains iterative procedures which bound the solution of initial value problems with the aid of interval analytical methods and possibilities for speeding up convergence.
openaire   +1 more source

Using solution sets for solving boundary value problems for ordinary differential equations

Nonlinear Analysis: Theory, Methods & Applications, 1991
The authors consider a differential equation of the type \(\dot x = f(t,x)\) together with the boundary condition \(x \in S\), where \(S\) is a subset of the space \(C\) of continuous functions. The existence of a solution for such a problem is deduced from the properties of the set of solutions of an associated family of problems, parameterized by an ...
ANICHINI, GIUSEPPE, CONTI, GIUSEPPE, ZECCA, PIETRO   +2 more
openaire   +1 more source

On the Convergence of a One-step Method for the Numerical Solution of an Ordinary Differential Inclusion

IMA Journal of Numerical Analysis, 1985
An initial value problem is analyzed for an ordinary differential inclusion for the case that the differential expression is contained in the image of a maximal monotone operator [\textit{H. Brézis}, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert (1973; Zbl 0252.47055)].
openaire   +2 more sources

Two solutions for ordinary differential inclusions with periodic boundary conditions

Journal of Mathematical Analysis and Applications
By employing variational methods for nonsmooth functionals, we establish the existence of two distinct solutions to an ordinary differential problem characterized by a set-valued reaction term. The investigation is conducted under the framework of periodic boundary conditions, which introduces additional challenges in the application of variational ...
Amoroso E., Bonanno G., Klun G., Morabito V.   +3 more
openaire   +1 more source

Transversality condition and optimization of higher order ordinary differential inclusions

Optimization, 2014
In the present paper, a Bolza problem of optimal control theory with a fixed time interval given by convex and nonconvex second-order differential inclusions (PH) is studied. Our main goal is to derive sufficient optimality conditions for Cauchy problem of sth-order differential inclusions. The sufficient conditions including distinctive transversality
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Eigenvalue inclusions for second-order ordinary differential operators by a numerical homotopy method

ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1990
An automated homotopy method, based on elementary estimates, is described for the computation of inclusion intervals for the first N eigenvalues of Sturm-Liouville problems with either separated or periodic boundary conditions. Interval arithmetic (with FORTRAN-SC subroutines) is used to deal with roundoff.
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A study of a self-adjoint coupled system of three nonlinear ordinary differential inclusions with cyclic anti-periodic boundary conditions

Discussiones Mathematicae Differential Inclusions, Control and Optimization
Summary: In this article, we shall deal with the existence theory for a self-adjoint coupled system of three nonlinear second-order ordinary differential inclusions with cyclic anti-periodic boundary conditions on an arbitrary domain. We consider convex valued as well as non-convex valued right-hand side of the given system and apply the standard fixed-
Ahmad, Bashir, Alsaedi, Ahmad, Almalki, Amal, Ntouyas, Sotiris K.   +3 more
openaire   +2 more sources