The description of all solutions to the relaxed commutant lifting problem in terms of an underlying contraction, obtained earlier in joint work of the author with A.E. Frazho and M.A. Kaashoek, is transformed into a linear fractional Redheffer state space form. Under certain additional conditions the coefficient functions in this representation are described explicitly in terms of the original ...

His basic criterion for disconjugacy turned out to be 1 0 is continuous and fal/P= °°, then the substitution t — fll/p transforms the first equation into one where p = l and the new f-interval is infinite. Thus this more general case reduces to Nehari's and again the criterion is 1 <X(o). However part of the whole picture seems to be lost by this transformation. If Ial...

We solve the suboptimal Nehari problem for a transfer function that has a state-space realization as a system-stable (input, output and inputoutput stable) well-posed linear system. We obtain an explicit solution in terms of the state-space parameters.

Abstract In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and nonlinear subcritical growth. Under very general assumptions on the data, prove existence at least two weak solutions have different energy sign. Our treatment is based fibering method in form Nehari manifold. We point out cover both...

We study the following singular problem involving p$(x)$-Laplace operator $\Delta_{p(x)}u= div(|\nabla u|^{p(x)-2}\nabla u)$, where $p(x)$ is a nonconstant continuous function, \begin{equation} \nonumber {{(\rm P_\lambda)}} \left\{\begin{aligned} - \Delta_{p(x)} u & = a(x)|u|^{q(x)-2}u(x)+ \frac{\lambda b(x)}{u^{\delta(x)}} \quad\mbox{in}\,\Omega,\\ &>0 \quad\mbox{in}\,\Omega, \\ =0 \quad\mbox{...

We present criteria of Hille-Nehari type for the half-linear dynamic equation (r(t)Φ(y∆))∆+p(t)Φ(yσ) = 0 on time scales. As a particular important case we get that there is a a (sharp) critical constant which may be different from what is known from the continuous case, and its value depends on the graininess of a time scale and on the coefficient r. As applications we state criteria for strong...

Abstract This paper presents a frequency domain solution to the delay-type Nehari problem. The solvability condition is formulated in terms of nonsingularities of three matrices. The optimal value is the maximal value such that one of the three matrices becomes singular when decreases from to . The all sub-optimal compensators are parameterized in a transparent structure with a modified Smith p...

The main purpose of this paper is to prove a sharp Sobolev inequality in an exterior of a convex bounded domain. There are two ingredients in the proof: One is the observation of some new isoperimetric inequalities with partial free boundary, and the other is an integral inequality (due to Duff [9]) for any nonnegative function under Schwarz equimeasurable rearrangement. These ingredients also ...

We complete the determination of how far convex maps can deform discs in each of the three classical geometries. The euclidean case was settled by Nehari in 1976, and the spherical case by Mej́ıa and Pommerenke in 2000. We find the sharp bound on the Schwarzian derivative of a hyperbolically convex function and thus complete the hyperbolic case. This problem was first posed by Ma and Minda in a ...