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### $\mathrm{ℬ𝒞}$-total stability and almost periodicity for some partial functional differential equations with infinite delay.

Journal of Applied Mathematics and Stochastic Analysis

### 2D-1D dimensional reduction in a toy model for magnetoelastic interactions

Applications of Mathematics

The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.

### 5-Shaped Bifurcation Curves of Nonlinear Elliptic Boundary Value Problems.

Mathematische Annalen

### A bifurcation theorem for noncoercive integral functionals

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the existence of critical points for noncoercive functionals, whose principal part has a degenerate coerciveness. A bifurcation result at zero for the associated differential operator is established.

### A bifurcation theory for periodic solutions of nonlinear dissipative hyperbolic equations

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### A bifurcation theory for some nonlinear elliptic equations

Colloquium Mathematicae

We deal with the problem ⎧ -Δu = f(x,u) + λg(x,u), in Ω, ⎨ (${P}_{\lambda }$) ⎩ ${u}_{\mid \partial \Omega }=0$ where Ω ⊂ ℝⁿ is a bounded domain, λ ∈ ℝ, and f,g: Ω×ℝ → ℝ are two Carathéodory functions with f(x,0) = g(x,0) = 0. Under suitable assumptions, we prove that there exists λ* > 0 such that, for each λ ∈ (0,λ*), problem (${P}_{\lambda }$) admits a non-zero, non-negative strong solution ${u}_{\lambda }\in {\bigcap }_{p\ge 2}{W}^{2,p}\left(\Omega \right)$ such that $li{m}_{\lambda \to 0⁺}||{u}_{\lambda }{||}_{{W}^{2,p}\left(\Omega \right)}=0$ for all p ≥ 2. Moreover, the function $\lambda ↦{I}_{\lambda }\left({u}_{\lambda }\right)$ is negative and decreasing in ]0,λ*[, where ${I}_{\lambda }$ is the energy functional related to (${P}_{\lambda }$).

### A blow up condition for a nonautonomous semilinear system.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### A blowup analysis of the mean field equation for arbitrarily signed vortices

Banach Center Publications

We study the noncompact solution sequences to the mean field equation for arbitrarily signed vortices and observe the quantization of the mass of concentration, using the rescaling argument.

### A blow-up mechanism for a chemotaxis model

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### A blow-up result for a viscoelastic system in ${ℝ}^{n}$.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### A blow-up result for nonlinear diffusion equations

Mathematica Slovaca

### A blowup result in a multidimensional semilinear thermoelastic system.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### A bound for the solutions of a basic elliptic system with non-linearity $q\geq 2$

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa Nota si dimostra un risultato enunciato nel § 5 della pubblicazione [4]. Per le soluzioni di un sistema ellittico base, con non-linearità $q\geq 2$, vale un principio di massimo analogo a quello dimostrato in [3] nel caso di non-linearità $q=2$.

### A boundary blow-up for sub-linear elliptic problems with a nonlinear gradient term.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### A boundary control problem with a nonlinear reaction term.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### A boundary Harnack principle for infinity-Laplacian and some related results.

Boundary Value Problems [electronic only]

### A Boundary Value Problem Connected with Response of Semi-space to a Short Laser Pulse

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper a mixed boundary value problem for the fourth order hyperbolic equation with constant coefficients which is connected with response of semi-space to a short laser pulse» and belongs to generalized Thermoelasticity is studied. This problem was considered by R. B. Hetnarski and J. Ignaczak, who established some important physical consequences. The present paper contains proof of the existence, uniqueness and continuous dependence of a solution on the datum, together with an effective...

### A boundary value problem for an elliptic equation with asymmetric coefficients in a non-schlicht domain.

Sibirskij Matematicheskij Zhurnal

### A brief introduction to homogenization and miscellaneous applications*

ESAIM: Proceedings

This paper is a set of lecture notes for a short introductory course on homogenization. It covers the basic tools of periodic homogenization (two-scale asymptotic expansions, the oscillating test function method and two-scale convergence) and briefly describes the main results of the more general theory of G−  or H−convergence. Several applications of the method are given: derivation of Darcy’s law for flows in porous media, derivation of the porosity...

### A capacity method for the study of Dirichlet problems for elliptic systems in varying domains

Rendiconti del Seminario Matematico della Università di Padova

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