These are well known and important theorems of Nehari, Ahlfors and Weill, and Krauss. We refer to Lehto's book [8] for a discussion of these results and for the properties of the Schwarzian that we shall need. The constants 2 in (1.1) and 6 in (1.3) are sharp. An example for the latter is the Koebe function k(z) = z(l — z)~ which has Schwarzian Sk(z) = — 6/(1 —z). We also remark that the class ...

hFih, x) > hFih, x) (0 è h < h < oo). In the course of this investigation the question arose whether a C2 solution of (1), with F subject to (2), is uniquely determined by the conditions (C) yia) = y'ib) = 0, y(x) > 0 for x E (a, b\. Nehari conjectured that this solution is unique under an additional condition on the behavior of Fit, x) as a function of x. The purpose of this note is to show th...

Abstract For studying the evolution of transverse deflection an extensible beam derived from connection mechanics, we investigate initial boundary value problem nonlinear equation with linear strong damping term, weak and source term. The key idea our analysis is to describe invariant manifold via Nehari manifold. To establish results global well-posedness solution, consider at three different ...

We consider the local and global well-posedness of the coupled nonlinear wave equations u tt − ∆u + g 1 (u t) = f 1 (u, v) v tt − ∆v + g 2 (v t) = f 2 (u, v), in a bounded domain Ω ⊂ R n with a nonlinear Robin boundary condition on u and a zero boundary conditions on v. The nonlinearities f 1 (u, v) and f 2 (u, v) are with supercritical exponents representing strong sources, while g 1 (u t) and...

In this paper, we consider the coupled Kirchhoff system in subcritical case and critical case. For case, first study least energy of limit by using Nehari manifold method exclude existence semi-trivial solutions. Then improve global compactness lemma to overcome loss compactness. Combining with linking theorem topological degree, construct a Palais-Smale sequence high level prove positive Moreo...

In this paper we study the following class of nonlocal problem involving Caffarelli-Kohn-Nirenberg type critical growth $$ L(u)-\lambda h(x)|x|^{-2(1+a)}u=\mu f(x)|u|^{q-2}u+|x|^{-pb}|u|^{p-2}u\quad \text{in } \mathbb R^N, $$% where $h(x)\geq 0$, $f(x)$ is a continuous function which may change sign, $\lambda, \mu$ are positive real parameters and $1&lt; q&lt; 2&lt; 4&lt; p=2N/[N+2(b-a)-2]$, $0...

In this paper, we investigate a class of p-Laplacian systems on locally finite graph $$G=(V,E)$$ . By exploiting the method Nehari manifold and some new analytical techniques, under suitable assumptions potentials nonlinear terms, prove that system admits ground state solution $$(u_{\lambda },v_{\lambda })$$ when parameter $$\lambda $$ is sufficiently large. Furthermore, consider concentration ...

In this paper we study quasilinear elliptic equations driven by the so-called double phase operator and with a nonlinear boundary condition. Due to lack of regularity, prove existence multiple solutions applying Nehari manifold method along truncation comparison techniques critical point theory. addition, can also determine sign (one positive, one negative, nodal). Moreover, as result independe...