We present criteria of Hille-Nehari-type for the linear dynamic equation (r(t)yΔ)Δ + p(t)yσ = 0, that is, the criteria in terms of the limit behavior of ( t a 1/r(s)Δs) ∫∞ t p(s)Δs as t→∞. As a particular important case, we get that there is a (sharp) critical constant in those criteria which belongs to the interval [0,1/4], and its value depends on the graininess μ and the coefficient r. Also ...

The problem of approximating a given scalar function φ on the unit circle T uniformly by functions analytic in the unit disk D has been attracting analysts for a long time (see [Kha], [RSh], [Ne], [AAK1-2], [CJ], [PKh]). It was shown in [Kha] that for a continuous function φ such a best approximation is unique while it is not unique in the general case. Later it turned out that this problem is ...

We obtain state-space formulas for the solution of the Nehari-Takagi/sub-optimal Hankel norm approximation problem for infinite-dimensional systems with a nonexponentially stable generator, via the method of J-spectral factorization. We make key use of a purely frequency domain solution of the problem. AMS mathematical subject classification numbers: 41A30, 47B35, 47B50, 47N70, 93B28.

In this paper, the existence and multiplicity of positive solutions for a critical singular elliptic system with concave and convex nonlinearity and sign-changing weight function, are established. With the help of the Nehari manifold, we prove that the system has at least two positive solutions via variational methods.

In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theor...

We consider a parametric double phase Dirichlet problem. In the reaction there is superlinear perturbation term which satisfies weak Nehari-type monotonicity condition. Using Nehari manifold method, we show that for all parameters below critical value, problem has at least three nontrivial solutions with sign information. The parameter value precisely identified in terms of spectrum lower expon...

In this paper, we extend the oscillation criteria that have been established by Hille [15] and Nehari [21] for second-order differential equations to third order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third order differential and difference equations, i.e. when T = R and T = N. We consider several examples to illustrate...

This note deals with a matricial Schur function arising from a completely indeterminate Nehari problem. The Schur algorithm is characterized by a unilateral shift for a Nehari sequence. c ⃝ 2017 Elsevier Inc. All rights reserved. MSC: 42C05; 42A56; 42A70

In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for an indefinite semilinear elliptic system ðEk;lÞ involving critical exponents and sign-changing weight functions. Using Nehari manifold, the system is proved to have at least two nontrivial nonnegative solutions when the pair of the parameters ðk;lÞ belongs to a certain subset of R. 20...

Hankel operators on the Hardy space of the disk, H (D) , can be studied as linear operators from H (D) to its dual space, as conjugate linear operators from H (D) to itself, or, in the viewpoint we will take here, as bilinear functionals on H (D) × H (D) . In that formulation, given a holomorphic symbol function b we consider the bilinear Hankel form, defined initially for f, g in P (D) , the s...