Results 261 to 270 of about 251,066 (317)

Existence of solutions and existence of optimal solutions. The quasi linear case

Rendiconti del Circolo Matematico di Palermo, 1985
Using Kakutani type fixed point theorems and monotone operator theory in new ways, the authors obtain existence theorems for abstract operator equations which include quasi-linear evolution equations and optimal control problems involving Cauchy-Dirichlet and Cauchy-Neumann equations.
Cesari, L., Hou, S. H.
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Existence of solutions to obstacle problems

Nonlinear Analysis: Theory, Methods & Applications, 1991
The purpose of this important paper is to study the question concerning the existence of solutions to obstacle problems. The pointwise regularity of solutions to certain obstacle problems (variational inequalities) is investigated. The authors have shown that, under certain conditions (\(\Omega\) is a bounded nonempty open set of \(\mathbb{R}^ n\) and \
Michael, J. H., Ziemer, William P.
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Existence of Solutions

2016
In this chapter, we describe and apply two boundary integral equation methods to solve the fundamental boundary value problems formulated in Sect.
Christian Constanda, Dale Doty, William Hamill   +2 more
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Existence of Solutions

2003
This chapter considers a single-input single-output (SISO) linear system under relay feedback and studies the existence of solutions to the system.
Qing-Guo Wang, Tong Heng Lee, Chong Lin
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Existence of Solutions

2017
This chapter proves existence of solutions to the inhomogeneous problem using the Schauder estimate and analyzes a generalized Kimura diffusion operator, L, defined on a manifold with corners, P. The discussion centers on the solution w = v + u, where v solves the homogeneous Cauchy problem with v(x, 0) = f(x) and u solves the inhomogeneous problem ...
Charles L. Epstein, Rafe Mazzeo
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Existence of solutions and existence of optimal solutions

1983
x 8 X = L2(J,V) , dx/dt 6 X* = L2(J,V*), t 6 J = [0,T], f 6 L2(J,V*), has at l e a s t one weak s o l u t i o n x 6 X, Ix[ ! R = al l f l x . . Thereby, we have obtained the well known existence of at least one solution z 6 X to the Cauchy problem with initial data x(0) = 0 for the linear evolution equation, by sole topological considerations.
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The existence of periodic solutions

1999
Abstract Suppose that the phase diagram for a differential equation contains a single, unstable equilibrium point and a limit cycle surrounding it, as in the case of the van der Pol equation. Then in practice all initial states lead to the periodic oscillation represented by the limit cycle.
D W Jordan, P Smith
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Existence of Solutions

2010
Existence and uniqueness of solutions of discrete–delay differential equations is established by the method of steps, appealing to classical ODE results. More general delay equations require a more general framework for existence and uniqueness. This includes some peculiar notation endemic to the subject and the identification of the appropriate state ...
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Existence of periodic solutions

Mathematical Notes, 1997
The author develops an apparatus for proving the existence of periodic solutions to differential equations \(y'(t)=Ay(t)+f(t,y(t))\) and to differential inclusions \(y'(t)\in Ay(t)+F(t,y(t))\). Here, \(A\) is a constant \(n\times n\) matrix, \(f\) is a Carathéodory function, and \(F\) is a Carathéodory multifunction. If the equation \(y'(t)=Ay(t)\) has
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Existence of Solutions

1984
To study the existence and uniqueness of solutions of optimal shape design problems, is interesting from the point of view of theory. However, at the present time, this problem has not been solved entirely; so we can only present some partial results.
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