and Applied Analysis 3 In order to describe our main result, we need to define Λ0 ( 2 − q ( p − q‖a‖L∞ ) 2−q / p−2 ( p − 2 ( p − q)‖b ‖Lq∗ ) S p 2−q /2 p−2 q/2 p > 0, 1.3 where ‖a‖L∞ supx∈RNa x , ‖b ‖Lq∗ ∫ RN |b x |qdx 1/q∗ and Sp is the best Sobolev constant for the imbedding of H1 R into L R . Theorem 1.1. Assume that a1 , b1 b2 hold. If λ ∈ 0, q/2 Λ0 , Ea,λb admits at least two positive solu...

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 ...

This paper describes some properties of a certain fibered hyperbolic 3manifold which arises ”in nature”; that is, as the cover of a closed manifold constructed by other means. Among other things, the main theorem answers in the affirmative the question of whether it is possible for a fibered hyperbolic manifold to be a double across a connected surface. (We first heard this question from Alan R...

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...

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.

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...

If2t is replaced by 2 in (1.1) then one obtains Nehari's original injectivity criterion. Nehari's result started what is by now a considerable amount of work in this area, see, e.g. ILl . Each of the present authors has been interested in theorems of this type, expecially in generalizations to higher dimensions, lOS1,2, C1,2]. What about one dimension? For a smooth real valued function on an in...

Let N be the set of all meromorphic functions f deened in the unit disc D that satisfy Nehari's univalence criterion (1 ? jzj 2) 2 jSf(z)j 2. In this paper we investigate certain properties of the class N. We obtain sharp estimates for the spherical distortion, and also a two-point distortion theorem that actually characterizes the set N. Finally, we study some aspects of the boundary behavior ...