Search

In this paper, we study the minimizing problem ... where ... N and ... is the Hardy- Littlewood-Sobolev upper critical exponent. Firstly, by using refinement of the Hardy- Littlewood-Sobolev inequality, we prove that Sp,1,α,μ is achieved in RN by a radially symmetric, nonincreasing and nonnegative function. Secondly, we give a estimation of extremal function. [ABSTRACT FROM AUTHOR]

The paper points out a relation between the distributional differential equation of the second order and the periodic problem for differential equations with statedependent impulses. The relation between these two problems is investigated and consequently the lower and upper functions method is extended to distributional differential equations. This enabled to get new existence results both for distributional equations and for non-autonomous periodic problems with state-dependent impulses. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following fourth-order three-point boundary value problem ... where n ∊ [1/3, 1). In spite of sign-changing Green's function, for arbitrary positive integer n (≥ 2), we still obtain the existence of at least n - 1 decreasing positive solutions to the above problem by imposing some suitable conditions on f . The main tool used is the fixed point index theory. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study higher-order (in space) anisotropic generalized Cahn-Hilliard models. In particular, we obtain well-posedness results, as well as the existence of the global attractor. Such models can have applications in biology, image processing, etc. We also give numerical simulations which illustrate the effects of the higher-order terms on the anisotropy. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new sufficient conditions for the oscillation of all solutions of third order nonlinear neutral difference equation of the form ... where α, β, and γ are the ratios of odd positive integers. Examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In the paper, we offer a new technique for investigation of properties of trinomial differential equations with positive and negative terms (b(t) (a{t)x'{t))')' + p{t)f{x{τ{t))) - q{t)h{x{σ(t))) = 0. We offer criteria for every solution to be oscillatory. We support our results with illustrative examples. [ABSTRACT FROM AUTHOR]