The effect of domain topology on the number of positive solutions for singular elliptic problems involving the Caffarelli-Kohn-Nirenberg inequalities

In this paper we consider the critical singular equation involving the Caffarelli-Kohn-Nirenberg inequalities of the type

     

Gagliardo–Nirenberg inequalities in regular Orlicz spaces involving nonlinear expressions

We consider a triple of N-functions (M,H,J) that satisfy the Δ^′-condition, and suppose that an additive variant of interpolation inequality holds

where , is an arbitrary set invariant with respect to external and internal dilations. We show that the above inequality implies its certain nonlinear variant involving the expressions and . Various generalizations of this inequality to the more general class of N-functions, measures and to higher order derivatives are also discussed and the examples are presented.     

Solutions with constant sign at infinity of a linear functional equation of infinite order

We investigate how the existence and behaviour of solutions φ with a constant sign of the equation

     

Growth conditions for oscillation of nonlinear differential equations with p-Laplacian

In this paper, oscillation criteria are established for all solutions of second-order nonlinear differential equations of the form

     

Infimum-convolution description of concentration properties of product probability measures, with applications

This paper is devoted to the concentration properties of product probability measures μ=μ₁⊗?⊗μn, expressed in term of dimension-free functional inequalities of the form

     

Weighted weak type inequalities for modified Hardy operators and geometric means operators in dimensions one and greater

We characterize the pairs of weights (u,v) such that the geometric mean operator G₁, defined for positive functions f on (0,∞) by

     

Integral inequalities for the Hilbert transform applied to a nonlocal transport equation

We prove several weighted inequalities involving the Hilbert transform of a function f(x) and its derivative. One of those inequalities,

is used to show finite time blow-up for a transport equation with nonlocal velocity.     

On the stability in periodic and almost periodic difference systems

In this paper we consider the system of difference equations

     

An approximate solution for nonlinear backward parabolic equations

We consider the backward parabolic equation

     

Existence of two solutions for the Bahri-Coron problem in an annular domain with a thin hole

We will show that the problem

     

Exact number of solutions of stationary reaction-diffusion equations

We study both existence and the exact number of positive solutions of the problem

     

Iterative equations in Banach spaces

Let X be a Banach space, let

     

Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption

We consider the Cauchy problem for the damped wave equation with absorption