Page 666 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts

TIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS

Convergence estimates for abstract second order differential equations
with two small parameters and lipschitzian nonlinearities

Galina Rusu, rusugalinamoldova@gmail.com
Moldova State University, Republic of Moldova

Coauthor: Andrei Perjan

In a real Hilbert space H endowed with the scalar product (·, ·) and the norm | · |, consider the
following Cauchy problem:

εuεδ(t) + δ uεδ(t) + Auεδ(t) + B uεδ(t) = f (t), t ∈ (0, T ), (Pεδ )
uεδ(0) = u0, uεδ(0) = u1,

where A : V ⊂ H → H, is a linear self-adjoint operator, V is a real Hilbert space endowed
with the norm || · ||, B is nonlinear A1/2 lipschitzian opeartor, u0, u1, f : [0, T ] → H and ε, δ
are two small parameters.

We investigate the behavior of solutions uεδ to the problem (Pεδ) in two different cases:
(i) ε → 0 and δ ≥ δ0 > 0, relative to the solutions to the following unperturbed system:

δlδ(t) + Alδ(t) + B lδ(t) = f (t), t ∈ (0, T ), (Pδ )
lδ(0) = u0;

(ii) ε → 0 and δ → 0, relative to the solutions to the following unperturbed system:

Av(t) + B v(t) = f (t), t ∈ [0, T ), (P0)

Geometric Hardy inequalities on starshaped sets

Bolys Sabitbek, sabytbek.bolys@gmail.com
Al-Farabi Kazakh National University, Kazakhstan

In this talk, we present the geometric Hardy inequalities on the starshaped sets in the Carnot
groups. Also, we obtain the geometric Hardy inequalities on half-spaces for general vector
fields.

Multiple entire solutions to the curl-curl problem with critical exponent

Jacopo Schino, jschino@impan.pl
Polish Academy of Sciences, Poland

Coauthors: Michał Gaczkowski, Jarosław Mederski

We prove the existence of infinitely many solutions with diverging energy to the problem
∇ × ∇ × U = |U|4U in R3.

We consider vector fileds of the form

u(x) −x2
U(x) = x1
r0

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