On positive solutions concentrating on spheres for the Gierer-Meinhardt system

We consider the stationary Gierer-Meinhardt system in a ball of R^N:

     

Quantum Hamiltonians with quasi-ballistic dynamics and point spectrum

Consider the family of Schrödinger operators (and also its Dirac version) on ?²(Z) or ?²(N)

     

Infinitely many solutions for some nonlinear scalar system of two elliptic equations

In this paper, we consider the elliptic system of two equations in H¹(RN)×H¹(RN):

     

Super-stationary set, subword problem and the complexity

Let Ω⊂{0,1}^N be a nonempty closed set with N={0,1,2,…}. For N={N₀<N₁<N₂<?}⊂N and ω∈{0,1}^N, define ω[N]∈{0,1}^N by and

     

Solutions to critical elliptic equations with multi-singular inverse square potentials

Let Ω be an open-bounded domain in R^N(N?3) with smooth boundary ∂Ω. We are concerned with the multi-singular critical elliptic problem

     

Existence of positive solutions for the Hénon equation involving critical Sobolev terms

Let N?3, ^2*=2N/(N−2) and Ω⊂RN be a bounded domain with a smooth boundary ∂Ω and 0∈Ω. Our purpose in this paper is to consider the existence of solutions of Hénon equation:

     

Positive clustered layered solutions for the Gierer-Meinhardt system

We consider the stationary Gierer-Meinhardt system in a ball of RN:

     

Multiple solutions for an elliptic problem related to vortex pairs

Let Ω be a bounded domain in RN (N?2), φ a harmonic function in . In this paper we study the existence of solutions to the following problem arising in the study of vortex pairs

     

Derivatives of the L-cosine transform

The L^p-cosine transform of an even, continuous function is defined by

     

Asymptotic properties of generalized Laguerre orthogonal polynomials

In the present paper we deal with the polynomials L_n^(α,M,N) (x) orthogonal with respect to the Sobolev inner product

     

Elliptic curves, modular forms, and sums of Hurwitz class numbers

Let H(N) denote the Hurwitz class number. It is known that if p is a prime, then

     

Existence of infinitely many solutions for sublinear elliptic problems

Let N?2 and be a bounded domain. In the present paper, we show the existence of infinity many solutions of nonlinear Dirichlet boundary value problem

     

Bounded positive entire solutions of singular quasilinear elliptic equations

Suppose that β?0 is a constant and that is a continuous function with R₊:=(0,∞). This paper investigates N-dimensional singular, quasilinear elliptic equations of the form

     

A min-max theorem for complex symmetric matrices

We optimize the form Re x^tTx to obtain the singular values of a complex symmetric matrix T. We prove that for ,

     

On the Laplace equation with dynamical boundary conditions of reactive-diffusive type

This paper deals with the Laplace equation in a bounded regular domain Ω of RN (N?2) coupled with a dynamical boundary condition of reactive-diffusive type. In particular we study the problem

     

A global multiplicity result for N-Laplacian with critical nonlinearity of concave-convex type

Let Ω⊂RN, N?2, be a bounded domain. We consider the following quasilinear problem depending on a real parameter λ>0: