A class of nonlinear evolution equations subjected to nonlocal initial conditions

We prove the existence of C⁰-solutions for a class of nonlinear evolution equations subjected to nonlocal initial conditions, of the form:

     

Dynkin's formula and large coupling convergence

Let H?1 be a selfadjoint operator in H, let J be a linear and bounded operator from (D(H^1/2),∥H^1/2·∥) to H_aux and for β>0 let be the nonnegative selfadjoint operator in H satisfying

     

Strong subtournaments containing a given vertex in regular multipartite tournaments

If x is a vertex of a digraph D, then we denote by d⁺(x) and d⁻(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by

     

Spectral analysis of a family of second-order elliptic operators with nonlocal boundary condition indexed by a probability measure

Let D⊂Rd be a bounded domain and let

     

Longest cycles in almost regular 3-partite tournaments

If D is a digraph, then we denote by V(D) its vertex set. A multipartite or c-partite tournament is an orientation of a complete c-partite graph. The global irregularity of a digraph D is defined by

     

Layered solutions for a semilinear elliptic system in a ball

We consider the following system of Schrödinger-Poisson equations in the unit ball B₁ of R³:

     

Non-spectral self-affine measure problem on the plane domain

The self-affine measure μM,D corresponding to an expanding integer matrix

     

A KAM theorem for one dimensional Schrödinger equation with periodic boundary conditions

In this paper, one-dimensional (1D) nonlinear Schrödinger equation

     

Positive clustered layered solutions for the Gierer-Meinhardt system

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

     

Orthogonal exponentials on the generalized three-dimensional Sierpinski gasket

The self-affine measure μM,D corresponding to the expanding integer matrix

     

Factorization in finitely generated domains

Let D be a Noetherian domain. Then it is well known that D is atomic, i.e. every non-zero non-unit a∈D possesses a factorization

     

A Tate cohomology sequence for generalized Burnside rings

We generalize the fundamental theorem for Burnside rings to the mark morphism of plus constructions defined by Boltje. The main observation is the following: If D is a restriction functor for a finite group G, then the mark morphism φ:D₊→D⁺ is the same as the norm map of the Tate cohomology sequence (over conjugation algebra for G) after composing with a suitable isomorphism of D⁺. As a consequence, we obtain an exact sequence of Mackey functors

     

On consecutive happy numbers

Let e?1 and b?2 be integers. For a positive integer with 0?aj<b, define