Multiple positive solutions to multipoint one-dimensional <Emphasis Type=Italic>p</Emphasis>-Laplacian boundary value problem with impulsive effects

In this paper, using a fixed point theorem on a convex cone, we consider the existence of positive solutions to the multipoint one-dimensional p-Laplacian boundary value problem with impulsive effects, and obtain multiplicity results for positive solutions.     

Periodic solutions to a <Emphasis Type=Italic>p</Emphasis>-Laplacian neutral Rayleigh equation with deviating argument

By using the coincidence degree theory, we study a type of p-Laplacian neutral Rayleigh functional differential equation with deviating argument to establish new results on the existence of T-periodic solutions.     

Infinitely many bounded solutions for the <Emphasis Type="Italic">p</Emphasis>-Laplacian with nonlinear boundary conditions

By applying a method due to Saint Raymond, we prove the existence of infinitely many weak solutions for a quasilinear elliptic partial differential equation, involving the p-Laplacian operator, coupled with a nonlinear boundary condition. Our main assumption is a suitable oscillatory behaviour of the nonlinearity either at infinity or at zero.     

The finite <Emphasis Type=Italic>p</Emphasis>-groups with <Emphasis Type=Italic>p</Emphasis> conjugacy classes of non-normal subgroups

Let ν(G) be the number of conjugacy classes of non-normal subgroups of a finite group G. The finite groups for which ν(G) ≤ 2 were determined by Dedekind and by Schmidt in the early times of group theory. On the other hand, if G is a finite p-group, La Haye and Rhemtulla have proved that either ν(G) ≤ 1 or ν(G) ≥ p. In this note, we determine all finite p-groups satisfying ν(G) = p for p > 2.     

On cyclic <Emphasis Type=Italic>p</Emphasis>-gonal Riemann surfaces with several <Emphasis Type=Italic>p</Emphasis>-gonal morphisms

Let p be a prime number, p > 2. A closed Riemann surface which can be realized as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. If the p-gonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic p-gonal Riemann surface. Accola showed that if the genus is greater than (p − 1)² the p-gonal morphism is unique. Using the characterization of p-gonality by means of Fuchsian groups we show that there exists a uniparametric family of cyclic p-gonal Riemann surfaces of genus (p − 1)² which admit two p-gonal morphisms. In this work we show that these uniparametric families are connected spaces and that each of them is the Riemann sphere without three points. We study the Hurwitz space of pairs (X, f), where X is a Riemann surface in one of the above families and f is a p-gonal morphism, and we obtain that each of these Hurwitz spaces is a Riemann sphere without four points.     

A necessary condition for non-abelian finite <Emphasis Type=Italic>p</Emphasis>-groups with second centre of order <Emphasis Type=Italic>p</Emphasis><Superscript>2</Superscript>

Let G be a non-abelian finite p-group such that |Z ₂(G)| = p ². In this paper we prove that each maximal subgroup M ≠ C _G (Z ₂(G)) is non-abelian and has cyclic centre.     

Infinitely many solutions of dirichlet problem for <Emphasis Type="Italic">p</Emphasis>-mean curvature operator

The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator: is considered, where Θ is a bounded domain in R ⁿ (n>p>1) with smooth boundary ∂Θ. Under some natural conditions together with some conditions weaker than (AR) condition, we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if . Supported by the National Natural Science Foundation of China (10171032) and the Guangdong Provincial Natural Science Foundation (011606).     

Existence of nontrivial solutions for <Emphasis Type=Italic>p</Emphasis>-Laplacian-Like equations

In this paper, we study the p-Laplacian-Like equations involving Hardy potential or involving critical exponent and prove the existence of one or infinitely many nontrivial solutions. The results of the equations discussed can be applied to a variety of different fields in applied mechanics.     

The <Emphasis Type=Italic>p</Emphasis>-adic quantum differential

We propose the Fredholm module structure on the space L₂(ℙ¹(ℚ_p)). We study the properties of the corresponding quantum Connes differential.     

Solutions of <Emphasis Type=Italic>p</Emphasis>-adic string equations

We review several purely mathematical results concerning boundary value problems for nonlinear pseudodifferential equations for p-adic closed and open strings in the tree approximation in the case d = 1. For the solutions of these problems, we present formulas establishing the relations between the numbers of their zeros, the multiplicities of the zeros, and the numbers indicating how many times the solutions change sign.     

A polynomial <Emphasis Type=Italic>p</Emphasis>-adic dynamical system

We completely describe the Siegel discs and attractors for the p-adic dynamical system f(x) = x ²ⁿ⁺¹ + axⁿ⁺¹ on the space of complex p-adic numbers.     

Nonlocal General Boundary Value Problems of Elliptic Type in <Emphasis Type=Italic>L</Emphasis><Superscript><Emphasis Type=Italic>p</Emphasis></Superscript> Cases

This paper is devoted to the study of operational second-order differential equations of elliptic type with nonregular coefficient-operator boundary conditions. In the framework of UMD spaces, we give some new results by using semi-groups and interpolation theory. We define two types of solutions: semi-strict and strict solutions. We then characterizes the existence and uniqueness of such solutions.