Browsing by Author "Vetro, Calogero"

Now showing 1 - 3 of 3

Access status: Open Access ,
A multiplicity theorem for parametric superlinear (p,q)-equations
(Wydawnictwa AGH, 2020) Onete, Florin-Iulian; Papageorgiou, Nikolaos Socrates; Vetro, Calogero
We consider a parametric nonlinear Robin problem driven by the sum of a $p$-Laplacian and of a $q$-Laplacian ($(p,q)$-equation). The reaction term is $(p-1)$-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.
Access status: Open Access ,
Galerkin-type minimizers to a competing problem for (p, q)-Laplacian with variable exponents
(Wydawnictwa AGH, 2026) Zhang, Zhenfeng; Ghasemi, Mina; Vetro, Calogero
This study focuses on a sequence of approximate minimizers for the functional \[J(u)=\int\limits_{\Omega}\sum\limits_{i=1}^{N}\frac{1}{p_{i}(x)}\bigg|\frac{\partial u}{\partial x_{i}}\bigg|^{p_{i}(x)}dx-\mu\int\limits_{\Omega}\sum\limits_{i=1}^{N}\frac{1}{q_{i}(x)}\bigg|\frac{\partial u}{\partial x_{i}}\bigg|^{q_{i}(x)}dx-\int\limits_{\Omega} F(u(x))dx,\] where $\Omega\subset\mathbb{R}^N$ ($N\geq 3$) is a bounded domain, and $p_i,q_i\in C(\overline{\Omega})$ with $1\lt p_i,q_i\lt +\infty$ for all $i \in \{1,\ldots,N\}$. We establish the convergence result to the infimum of $J(u)$ when $F:\mathbb{R}\to\mathbb{R}$ is a locally Lipschitz function of controlled growth, following the Galerkin method. As an application, we establish the existence of solutions to a class of Dirichlet inclusions associated to the functional.
Access status: Open Access ,
On a Robin (p,q)-equation with a logistic reaction
(Wydawnictwa AGH, 2019) Papageorgiou, Nikolaos Socrates; Vetro, Calogero; Vetro, Francesca
We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a $p$-Laplacian and of a $q$-Laplacian ($(p,q)$-equation) plus an indefinite potential term and a parametric reaction of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter $\lambda \gt 0$ varies. Also, we show that for every admissible parameter $\lambda \gt 0$, the problem admits a smallest positive solution.