Tuesday, January 30, 2024 — 12:00 pm — aula M2.4, edificio Matematica
Some recent results on boundary value problems for differential and integro-differential equations involving nonlinear differential operators
Abstract:
The talk concerns some results, obtained jointly with a research team in Ancona, concerning the existence and non-existence of solutions to boundary value problems for differential equation governed by nonlinear differential operators of the type
$$ \Phi(k(t)x’(t))’ = f(t,x(t),x’(t))$$
where $\Phi$ is the so-called $\Phi-$laplacian operator, the term $k(t)$ is nonnegative (possibly vanishing at some point), and $f$ is Caratheodory.
Developments of this study also concern functional differential equations and integro-differential equations of the type
$$ \Phi(k(t)x’(t))’ = f\left(t,\int_0^t x(s)ds, x(t) ,x’(t)\right).$$