Eigenvalues of p(x)-Laplacian Dirichlet problem

This paper studies the eigenvalues of the p(x)-Laplacian Dirichlet problem

     

A Knobloch-type result for p(t)-Laplacian systems

We consider the periodic boundary value problem of ordinary differential systems with p(t)-Laplacian of the form

     

L-Poisson integral representations of solutions of the Hua system on the bounded symmetric domain SU(n,n)/S(U(n)×U(n))

Let positive definite} be the matrix ball of rank n and let H_D be the associated Hua operator. For a complex number λ, such that Reiλ>n−1 we give a necessary and sufficient condition on solutions F of the following Hua system of differential equations on D:

     

Tauberian theorems for double sequences that are statistically summable (C,1,1)

Let be a double sequence of real or complex numbers, and set

     

Dynamics of the w function and primes

We begin by defining a function w on the set

     

On the number of solutions of Goormaghtigh equation for given x and y

In this note, we extend a result obtained by Bugeaud and Shorey in Pacific J. Math.207 (2002) 61-75. In fact, we show that the Goormaghtigh equation

     

On the equipartition of energy for the critical NLW

We study some qualitative properties of global solutions to the following focusing and defocusing critical NLW:

     

When subset-sums do not cover all the residues modulo p

Let . We prove that a subset of , where p is a prime number, with cardinality larger than such that its subset sums do not cover has an automorphic image which is rather concentrated; more precisely, there exists s prime to p such that

     

On the asymptotic behavior of xn+1=anxn/xn−1

We investigate the asymptotic behavior of solutions of a separable difference equation of the form

     

Necessary and sufficient conditions of existence for a system involving the p-Laplacian (1<p<N)

In this work, we study the existence of positive solutions for the system

     

Higher-order asymptotic formula for the eigenvalues of Sturm-Liouville problem with n turning points

In this paper, we investigate the asymptotic behavior of the differential equation

     

L stability estimate for a one-dimensional Boltzmann equation with inelastic collisions

In this paper, we study the L¹ stability of a one-dimensional Boltzmann equation on the line with inelastic collisions in Rend. Sem. Mat. Fis. Milano 67 (1997) 169-179. Under the suitable assumptions on the initial data, we construct a nonlinear functional which measures L¹ distance between two mild solutions, and is nonincreasing in time t. Using the time-decay estimate of , we show that mild solutions are L¹-stable:

     

On the parity of exponents in the standard factorization of n!

Let p₁,p₂,… be the sequence of all primes in ascending order. The following result is proved: for any given positive integer k and any given , there exist infinitely many positive integers n with

     

Some Zygmund type L inequalities for polynomials

Let p(z) be a polynomial of degree n which does not vanish in |z|<k. It is known that for each q>0 and k?1,