On existence and multiplicity for Schrödinger–Poisson systems involving weighted sublinear nonlinearities

We deal with existence and multiplicity for the following class of nonhomogeneous Schrödinger–Poisson systems \begin{equation*} \begin{cases} -\Delta u + V(x) u + K(x) \phi(x) u = f(x, u) + g(x) \quad & \text{in } \mathbb{R}^3, \\ -\Delta \phi = K(x) u^2 \quad & \text{in } \mathbb{R}^3, \end{cases} \end{equation*} where $V, K: \mathbb{R}^3 \rightarrow \mathbb{R}^+$ are suitable potentials and $f: \mathbb{R}^3 \times \mathbb{R} \rightarrow \mathbb{R}$ satisfies sublinear growth assumptions involving a finite number of positive weights $W_i$, $i= 1,\dots,r$ with $r \geq 1$. By exploiting compact embeddings of the functional space on which we work in every weighted space $L_{W_i}^{w_i}(\mathbb{R}^3)$, $w_i \in (1, 2)$, we establish existence by means of a generalized Weierstrass theorem. Moreover, we prove multiplicity of solutions if $f$ is odd in $u$ and $g(x) \equiv 0$ thanks to a variant of the symmetric mountain pass theorem stated by R. Kajikiya for subquadratic functionals

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal