In this article, we study the existence and multiplicity of positive solutions for the quasi-linear elliptic problems involving critical Sobolev exponent and a Hardy term. The main tools adopted in our proofs are the concentration compactness principle and Nehari manifold.

We employ Nehari manifold methods and critical point theory to study the existence of nontrivial homoclinic solutions of discrete p-Laplacian equations with a coercive weight function and superlinear nonlinearity. Without assuming the classical Ambrosetti-Rabinowitz condition and without any periodicity assumptions, we prove the existence and multiplicity results of the equations.

We study the existence of ground states a Schrödinger–Poisson–Slater type equation with pure power nonlinearity. By carrying out constrained minimization on special manifold, which is combination Pohozaev manifold and Nehari we obtain state solutions this system.

‎using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{r}^n$‎. ‎the existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $v(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.

The Schwarzian derivative of an analytic function is a basic tool in complex analysis. It appeared as early as 1873, when H. A. Schwarz sought to generalize the Schwarz-Christoffel formula to conformal mappings of polygons bounded by circular arcs. More recently, Nehari [5, 6, 7] and others have developed important criteria for global univalence in terms of the Schwarzian derivative, exploiting...

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, 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