Derivatives of the L-cosine transform

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

     

Global branch from the second eigenvalue for a semilinear Neumann problem in a ball

Let (n?3) be a ball, and let f∈C³. We are concerned with the Neumann problem

     

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 ,

     

Simultaneous Diophantine approximation on manifolds and Hausdorff dimension

Let M be an m-dimensional, C^k manifold in , for any , and for any τ>0 let

     

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

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

     

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:

     

Refinement type equations and Grincevi?jus series

We consider L¹-solutions of the following refinement type equations

     

Norm estimates of almost Mathieu operators

We estimate the norm of the almost Mathieu operator , regarded as an element in the rotation C^*-algebra . In the process, we prove for every λ∈R and the inequality

     

Adams' inequalities for bi-Laplacian and extremal functions in dimension four

Let Ω⊂R⁴ be a smooth oriented bounded domain, be the Sobolev space, and be the first eigenvalue of the bi-Laplacian operator Δ². Then for any α: 0?α<λ(Ω), we have

     

Exceptional congruences for the coefficients of certain eta-product newforms

Let F(z)=∑_n=1^∞a(n)qⁿ denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that

     

Estimates of majorizing sequences in the Newton-Kantorovich method: A further improvement

Let be an operator, with X and Y Banach spaces, and f^′ be Hölder continuous with exponent θ. The convergence of the sequence of Newton-Kantorovich approximations

     

Existence and multiplicity results for a fourth order mean field equation

In this article we consider the following fourth order mean field equation on smooth domain Ω?R⁴:

     

Regularity results for a class of obstacle problems under nonstandard growth conditions

We prove regularity results for minimizers of functionals in the class , where is a fixed function and f is quasiconvex and fulfills a growth condition of the type

L⁻¹|z|^p(x)?f(x,ξ,z)?L(1+|z|^p(x)),     

Schröder equation and commuting functions on the circle

We show that if is a homeomorphism of the unit circle S¹ and the rotation number α(F) of F is irrational, then the Schröder equation

     

On the stability of limit cycles for planar differential systems

We consider a planar differential system , , where P and Q are C¹ functions in some open set U⊆R², and . Let γ be a periodic orbit of the system in U. Let f(x,y):U⊆R²→R be a C¹ function such that