Showing papers on "Strongly monotone published in 1986"
TL;DR: In this paper, the authors obtained sufficient conditions for an autonomous functional differential equation to generate a strongly monotone semi-low on a suitable state space, and established a very striking relationship between such functional differential equations and corresponding ordinary differential equations.
182 citations
50 citations
45 citations
TL;DR: It is shown that every graph on n nodes can be partitioned by a number of complete bipartite graphs with O(n2/log n) nodes with no edge belonging to two of them, and an upper bound for the monotone formula size of quadratic functions is obtained.
Abstract: We show that every graph on n nodes can be partitioned by a number of complete bipartite graphs with O(n
2/log n) nodes with no edge belonging to two of them Since each partition corresponds directly to a monotone formula for the associated quadratic function we obtain an upper bound for the monotone formula size of quadratic functions Our method extends to uniform hypergraphs with fixed range and thus to homogeneous functions with fixed length of prime implicants Finally we give an example of a quadratic function where each monotone formula built from arbitrary partitions of the graph (double edges allowed) is not optimal That means we disprove the single-level-conjecture for formulae
35 citations
TL;DR: In this article, the authors show that the choice of initial functions cannot be arbitrary for the extremal solution to hold, and they then develop a monotone technique to obtain extremal solutions.
Abstract: In proving existence of extremal solutions for delay differential equations, one usually assumes nondecreasing property on the function involved without which the proof breaks down. Our main purpose, in this paper, is to remove the monotone assumption by proving a new comparison result which is required in the analysis and which avoids the standard line of argument. Furthermore, our comparison theorem shows that the choice of initial functions cannot be arbitrary for the results to hold. Using this result we then develop monotone technique to obtain extremal solutions.
16 citations
TL;DR: In this paper, the authors untersuchen den 1-monotonen Operator TK B x E*, fE TK X [I,!] E K(x, x), der uber das Subdifferential einer konkav-konvexen Sattelfunktion K definiert ist.
Abstract: \\Vir untersuchen den 1monotonen Operator TK B x E*, fE TK X [—I,!] E K(x, x), der uber das Subdifferential einer konkav-konvexen Sattelfunktion K definiert ist. Unsere Uber. legungen werdon durch die Tatsache motiviert, daB jeder maximal monotone Operator A in der Form A = TK darstellbar ist. Wir zeigen, daB TK genau dunn maximal iionoton ist, wenu K in einer abgeschwächten Form schiefsynsmetrisch 1st. Dies erlaubt eine Verillgemmicilerung früher erzielter Ergebnisse.
13 citations
TL;DR: In this paper, it was shown that the clone of all nonsurjective functions on R8 is finitely generated, i.e., it is possible to construct a monotone function on the 8-element bounded tower.
Abstract: Let R8 denote the 8-element bounded tower. G. Tardos has shown that C(R8), the clone of all monotone functions on R8, is not finitely generated. In this paper we show that the clone of all nonsurjective functions is finitely generated.
8 citations
TL;DR: In this article, the authors studied the solvability of nonlinear random equations involving operators of the form L + T, where L is a maximal monotone random operator from Ω × X into X∗ and T : Ω → X → X ∗ is a random operator of monotonous type.
5 citations
01 Jan 1986
TL;DR: In this paper, for the θ-method, θ = 1/2(2+ζτV), 0 0, it was shown that τ → 0, where τ is the maximal timestep for an arbitrary choice of the sequence of timesteps and with no further condition on F, and an estimate O(τ2) under some additional conditions.
Abstract: For evolution equation with a monotone operator we derive unconditional stability and error estimates valid for all times. θ-method, For the θ=1/2(2+ζτV), 0 0), we prove an error estimate O(τ4/3), τ → 0, if V=1/3, where τ is the maximal timestep for an arbitrary choice of the sequence of timesteps and with no further condition on F, and an estimate O(τ2) under some additional conditions. The first result is an improvement over the implicit midpoint method (θ=½), for which an order reduction to O(τ) may occur.
2 citations
1 citations
Book•
01 Jan 1986
TL;DR: In this article, the authors provide a comprehensive survey of the general theory of nonlinear problems in fluid mechanics, including free boundary problems, boundary value problems, and boundary integral equations of elasticity in weighted spaces.
Abstract: Mathematical and numerical study of nonlinear problems in fluid mechanics.- Free boundary problems in fluid dynamics.- Method of rothe in evolution equations.- Boundary value problems in weighted spaces.- Critical point theory and nonlinear differential equations.- Ordinary linear differential equations - A survey of the global theory.- Numerical and theoretical treating of evolution problems by the method of discretization in time.- Algorithms for the inclusion of solutions of ordinary initial value problems.- Recent developments in the theory of function spaces.- On properties of oscillatory solutions of non-linear differential equations of the n-th order.- Uniqueness without continuous dependence.- Connections in scalar reaction diffusion equations with neumann boundary conditions.- On a certain boundary value problem of the third order.- On nonparasite solutions.- Uniform zeros for beaded strings.- Perron intergaral, perron product integral and ordinary linear differential equations.- On the zeros of some special functions: Differential equations and nicholson-type formulas.- Surjectivity and boundary value problems.- Some problems concerning the equivalences of two systems of differential equations.- Linear perturbations of general disconjugate equations.- On optimal control of systems with interface side conditions.- A description of blow-up for the solid fuel ignition model.- Spectral analysis of non-self-adjoint elliptic operators.- On the Mountain Pass Lemma.- On uniqueness and stability of steady-state carrier distributions in semiconductors.- Partial regularity of minimizers.- Periodic solutions of partial differential equations with hysteresis.- Stability and bifurcation problems for reaction-diffusion systems with unilateral conditions.- Boundary integral equations of elasticity in domains with piecewise smooth boundaries.- Higher regularity of weak solutions of strongly nonlinear elliptic equations.- Some regularity results for quasilinear parabolic systems.- Classical boundary value problems for Monge-Ampere type equations.- Qualitative properties of the solutions to the navier-stokes equations for compressible fluids.- On Gel'fand's method of chasing for silving multipoint boundary value problems.- Stability and error estimates valid for infinite time, for strongly monotone and infinitely stiff evolution equations.- Recent results in the approximation of free boundaries.- Finite element solution of a nonlinear diffusion problem with a moving boundary.- Analysis of thacker's method for solving the linearized shallow water equations.- The convergence of a new method for calculating lower bounds to eigenvalues.- Bifurcation analysis of stimulated brillouin scattering.- Superconvergence results for linear triangular elements.- Mixed finite element in 3D in H(div) and H(curl).- Free boundary problems for stokes' flows and finite element methods.- Enclosing methods for perturbed boundary value problems in nonlinear difference equations.- Error estimates for finite element methods for semilinear parabolic problems with nonsmooth data.- Singularities in two- and three-dimensional elliptic problems and finite element methods for their treatment.- Some new convergence results in finite element theories for elliptic problems.- Mathematical solution of direct and inverse problem for transonic cascade flows.- Einige Anwendungen der Mehrdimensionalen Approximationstheorie zur Losungseinschliessung bei Randwertaufgaben.- A posteriori estimations of approximate solutions for some types of boundary value problems.- Nonlinear dynamics systems - bifurcations, continuation methods, periodic solutions.- The rothe method for nonlinear hyperbolic problems.- Some solved and unsolved canonical problems of diffraction theory.- Entropy compactification of the transonic flow.- The global existence of weak solutions of the mollified system of equations of motion of viscous compressible fluid.- Bifurcations near a double eigenvalue of the rectangular plate problem with a domain parameter.- Delay makes problems in population modelling.
TL;DR: In this article, a slightly modified method was developed to solve a generalized complementarity problem with a Lipschitz continuous, pseudomonotone, and integrable function.
Abstract: In an earlier paper, the author proposed an iterative method for generalized complementarity problems with Lipschitz continuous and strongly monotone functions. Here we show that a slightly modified method can be developed to solve a generalized complementarity problem with a Lipschitz continuous, pseudomonotone, and integrable function.