An explicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of an infinite family of nonexpansive mappings

Let H be a Hilbert space and C be a nonempty closed convex subset of H, {T_i}_i∈N be a family of nonexpansive mappings from C into H, G_i:C×C→R be a finite family of equilibrium functions (i∈{1,2,…,K}), A be a strongly positive bounded linear operator with a coefficient and -Lipschitzian, relaxed (μ,ν)-cocoercive map of C into H. Moreover, let , {α_n} satisfy appropriate conditions and ; we introduce an explicit scheme which defines a suitable sequence as follows:

     

Mann iteration of Cesàro means for asymptotically non-expansive mappings

Let K be a nonempty closed convex subset of a uniformly convex Banach space E with a uniformly Gâteaux differentiable norm. Suppose that T:K→K is an asymptotically non-expansive mapping and for arbitrary initial value x₀∈K, we will introduce the Mann iteration of its Cesàro means:

     

On a new class of elliptic systems with nonlinearities of arbitrary growth

We guarantee the existence of infinitely many different pairs of solutions to the system

     

Global bifurcation for equations involving nonhomogeneous operators in an unbounded domain

We study the structure of the set of solutions of a nonlinear equation involving nonhomogeneous operators:

     

Variational method based on finite dimensional approximation in a generalized prescribed mean curvature problem

An elementary existence proof based on variational and finite dimensional approximation methods is proposed for nontrivial solutions of the generalized prescribed mean curvature boundary value problem

     

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

     

Multiplicity results for a class of gradient systems depending on two parameters

In this paper we prove the existence of at least three solutions for a class of two-point boundary value systems of the type

     

A nonlinear parabolic equation backward in time: Regularization with new error estimates

Consider a nonlinear backward parabolic problem in the form

     

An analytic approach to purely nonlocal Bellman equations arising in models of stochastic control

Given a bounded domain Ω⊂Rd and two integro-differential operators L¹, L² of the form we study the fully nonlinear Bellman equation

(0.1)     

Spectral theory for perturbed Krein Laplacians in nonsmooth domains

We study spectral properties for HK,Ω, the Krein-von Neumann extension of the perturbed Laplacian −Δ+V defined on , where V is measurable, bounded and nonnegative, in a bounded open set Ω⊂Rn belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class C1,r, r>1/2. In particular, in the aforementioned context we establish the Weyl asymptotic formula

     

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

     

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

     

Galois closure and Lagrangian varieties

Let X be a complex projective variety and consider the morphism