In this work we extend an inequality of Nehari to the eigenvalues of weighted quasilinear problems involving the p-laplacian when the weight is a monotonic function. We apply it to different eigenvalue problems.

We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters (λ, μ) belongs to a suitable subset of R.

This article concerns the diffusion system ∂tu−∆xu + V (x)u = g(t, x, v), −∂tv −∆xv + V (x)v = f(t, x, u), where z = (u, v) : R × RN → R2, V (x) ∈ C(RN , R) is a general periodic function, g, f are periodic in t, x and asymptotically linear in u, v at infinity. We find a minimizing Cerami sequence of the energy functional outside the Nehari-Pankov manifold N and therefore obtain ground state so...

We establish the topological s-cobordism surgery sequence for any closed oriented 4-manifold X homotopy equivalent to a connected sum X1# · · ·#Xn such that each topological 4-manifold Xi has fundamental group Γi of class SA. As a corollary, given Γi in a subclass ECS, if Γi is torsionfree and π2(Xi)⊗ Z2 = 0 (e.g. Xi aspherical), then X is topologically s-rigid. An application is an s-fibering ...

for some α (0≤α< 1). We say that f(z) is in the class ∑C(α) of such functions. The class ∑∗(α) and various other subclasses of ∑ have been studied rather extensively by Nehari and Netanyahu [9], Clunie [4], Pommerenke [11, 12], Miller [7], Royster [13], and others (cf., e.g., Bajpai [2], Goel and Sohi [6], Mogra et al. [8], Uralegaddi and Ganigi [15], Cho et al. [3], Aouf [1], and Uralegaddi an...

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...