Zobrazeno 1 - 10
of 226
pro vyhledávání: '"Punzo, Fabio"'
Autor:
Punzo, Fabio, Svagna, Marcello
We investigate the uniqueness, in suitable weighted $\ell^p$ spaces, of solutions to the Schr\"odinger equation with a potential, posed on infinite graphs. The potential can tend to zero at infinite with a certain rate.
Externí odkaz:
http://arxiv.org/abs/2407.05757
We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator $\mathcal{L} = -\Delta+(-\Delta)^s$, with a power-like source term. We show that the so-called Fujita phenomenon holds, and the
Externí odkaz:
http://arxiv.org/abs/2406.17731
We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function $f(u)$. We always assume that the infimum of the spectrum of the Laplace ope
Externí odkaz:
http://arxiv.org/abs/2406.15069
Autor:
Biagi, Stefano, Punzo, Fabio
We investigate the validity of the Phragm\`en-Lindel\"of principle for a class of elliptic equations with a potential, posed on infinite graphs. Consequently, we get uniqueness, in the class of solutions satisfying a suitable growth condition at infi
Externí odkaz:
http://arxiv.org/abs/2406.06505
We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper bound on the Laplacian of the distance and a suitable weighted space-t
Externí odkaz:
http://arxiv.org/abs/2404.12058
We consider the porous medium equation (PME) on complete noncompact manifolds $M$ of nonnegative Ricci curvature. We require nonparabolicity of the manifold and construct a natural space $X$ of functions, strictly larger than $L^1$, in which the Gree
Externí odkaz:
http://arxiv.org/abs/2402.18706
We study mixed local and nonlocal elliptic equation with a variable coefficient $\rho$. Under suitable assumptions on the behaviour at infinity of $\rho$, we obtain uniqueness of solutions belonging to certain weighted Lebsgue spaces, with a weight d
Externí odkaz:
http://arxiv.org/abs/2307.02209
We study semilinear elliptic inequalities with a potential on infinite graphs. Given a distance on the graph, we assume an upper bound on its Laplacian, and a growth condition on a suitable weighted volume of balls. Under such hypotheses, we prove th
Externí odkaz:
http://arxiv.org/abs/2306.03609
We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on the potential, we prove that the unique bounded solution is $u\equiv 0$
Externí odkaz:
http://arxiv.org/abs/2304.00786
Stochastic incompleteness of a Riemannian manifold $M$ amounts to the nonconservation of probability for the heat semigroup on $M$. We show that this property is equivalent to the existence of nonnegative, nontrivial, bounded (sub)solutions to $\Delt
Externí odkaz:
http://arxiv.org/abs/2301.07942