this paper is concerned with the existence of multiple positive‎ ‎solutions for a quasilinear elliptic system involving concave-convex‎ ‎nonlinearities‎ ‎and sign-changing weight functions‎. ‎with the help of the nehari manifold and palais-smale condition‎, ‎we prove that the system has at least two nontrivial positive‎ ‎solutions‎, ‎when the pair of parameters $(lambda,mu)$ belongs to a certai...

f " ' f " 2 where Sf := (p-) 1⁄2 (iv) denotes the Schwarzian derivative, and that this result is sharp, as the function f(z) = 1⁄2 log 11 z + z shows. Tile method of the proof does not give all sharp functions. We shall show that the sharp function is essentially unique using another approach implying Nehari's result. This shows furthermore that all convex domains except of parallel strip domai...

Hankel norm and Nehari-type approximation problems arise in model reduction and H1-control theory. Existing solutions to the discrete-time version of these problems may be derived using a standard state-space framework, but the resulting solution formulas require an invertible A-matrix. As a further complication, the D-matrix in the representation formula for all solutions becomes unbounded in ...

Abstract. We give a full extension of (one version of) the celebrated "AAK-theorem" on Hankel operators, to the case of weighted l-spaces with increasing weights. This theorem was conjectured in [3], and it improves earlier work by S. Treil and A. Volberg, [8]. We also show that the corresponding extension of the classical formulation of the "AAK-theorem" fails, and show that this is a conseque...

and Applied Analysis 3 Theorem 1.3 see 5 . There exists λ0 > 0 such that 1.4 admits exactly two solutions for λ ∈ 0, λ0 , exactly one solution for λ λ0, and no solution for λ > λ0. To proceed, wemake somemotivations of the present paper. Recently, in 6 the author has considered 1.2 with subcritical nonlinearity of concave-convex type, g ≡ 1, and f is a continuous function which changes sign in ...

In this paper, we deal with the existence and nonexistence of nonnegative nontrivial weak solutions for a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and a sign-changing function. Some existence results are obtained by splitting the Nerahi manifold and by exploring some properties of the best Hardy-Sobolev constan...

This note is a sequel to our paper [OS] where we generalized the Schwarzian derivative to conformal mappings of Riemannian manifolds. There we found that many of the phenomena familiar from the classical theory have counterparts in the more general setting. Here we advance this another step by giving a generalization of the well known univalence criterion of Nehari [N]. Despite its relatively a...