Calogero Vetro
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Calogero Vetro has a total of 111 co-authors. Here are the top co-authors by number of shared publications:
- Francesca Vetro
Scientific Research Center, Baku Engineering University, Khirdalan City, Baku, Azerbaijan
39 shared publications - Nikolaos S. Papageorgiou
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
31 shared publications - Bessem Samet
Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia
26 shared publications Francesca Vetro
11 shared publicationsNikolaos S. Papageorgiou
11 shared publicationsMohamed Jleli
King Saud University
9 shared publications
Latest Publications
- Open Access
- 1 January 2027
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
- Vol. 35, 529-551
Existence and uniqueness for a coupled McKean–Vlasov stochastic differential variational system with locally Hölder diffusion
We study a coupled system consisting of a one-dimensional McKean–Vlasov stochastic variational inequality and a Hilbert space evolution equation. The coefficients are formulated in terms of the state, the law of the variational component, and the Hilbert space component. The drift satisfies a coercive Lyapunov condition and is locally Lipschitz in the state, law, and Hilbert space variables. The diffusion is bounded and satisfies a Yamada–Watanabe type locally Hölder condition. For each frozen law flow we construct the coupled variational system by Yosida–Moreau regularization. Uniform exponential moment estimates, compactness of law flows, and continuity of the frozen-law map allow us to apply Schauder's fixed point theorem and obtain existence. Pathwise uniqueness is obtained by a localization and Osgood argument.
- 1 January 2027
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
- Vol. 35, 529-551
Open AccessExistence and uniqueness for a coupled McKean–Vlasov stochastic differential variational system with locally Hölder diffusion
We study a coupled system consisting of a one-dimensional McKean–Vlasov stochastic variational inequality and a Hilbert space evolution equation. The coefficients are formulated in terms of the state, the law of the variational component, and the Hilbert space component. The drift satisfies a coercive Lyapunov condition and is locally Lipschitz in the state, law, and Hilbert space variables. The diffusion is bounded and satisfies a Yamada–Watanabe type locally Hölder condition. For each frozen law flow we construct the coupled variational system by Yosida–Moreau regularization. Uniform exponential moment estimates, compactness of law flows, and continuity of the frozen-law map allow us to apply Schauder's fixed point theorem and obtain existence. Pathwise uniqueness is obtained by a localization and Osgood argument.
- Open Access
Mathematics: Feature Papers 2025
This Special Issue of the journal Symmetry is dedicated to recent mathematics investigations, showcasing a collection of twenty research works and four reviews in different fields of mathematics
Open AccessMathematics: Feature Papers 2025
This Special Issue of the journal Symmetry is dedicated to recent mathematics investigations, showcasing a collection of twenty research works and four reviews in different fields of mathematics
- 18 May 2026
- Published by Hacettepe University in Hacettepe Journal of Mathematics and Statistics
- Vol. 55 (Advanced O) , 1580-1593
Existence of Projected solutions for a quasi-equilibrium problem with applications
This article studies a quasi-equilibrium problem (QEP, for short) in an infinite dimensional Banach space $X$. Under very mild assumptions, we establish nonemptiness and compactness of projected solution set to (QEP), both in the cases when $X$ is reflexive or not. The main strategy is based on the Michael selection theorem, the Schauder fixed-point theorem, an approximating technique and the concept of approximatively compactness. As application of the obtained results, we focus on three problems with non-self and implicit constraints which are, respectively, a quasi-variational-hemivariational inequality, a quasi-optimization problem, and a generalized Nash equilibrium problem.- 18 May 2026
- Published by Hacettepe University in Hacettepe Journal of Mathematics and Statistics
- Vol. 55 (Advanced O) , 1580-1593
Existence of Projected solutions for a quasi-equilibrium problem with applications
This article studies a quasi-equilibrium problem (QEP, for short) in an infinite dimensional Banach space $X$. Under very mild assumptions, we establish nonemptiness and compactness of projected solution set to (QEP), both in the cases when $X$ is reflexive or not. The main strategy is based on the Michael selection theorem, the Schauder fixed-point theorem, an approximating technique and the concept of approximatively compactness. As application of the obtained results, we focus on three problems with non-self and implicit constraints which are, respectively, a quasi-variational-hemivariational inequality, a quasi-optimization problem, and a generalized Nash equilibrium problem.- Open Access
- 20 March 2026
- Published by Wiley in Mathematical Methods in the Applied Sciences
Weak Solutions for a Class of Nonlocal Singular Problems Over the Nehari Manifold
In this paper, we consider a nonlocal model of dilatant non‐Newtonian fluid with a Dirichlet boundary condition. By using the Nehari manifold and fibering map methods, we obtain the existence of at least two weak solutions, with sign information. In detail, we construct two local minimizers of the energy functional associate to the main problem on proper Nehari submanifolds; in this way, we bypass the singularity to get boundedness below and coercivity of the functional. Then, we conclude that such minimizers correspond to weak solutions.
- 20 March 2026
- Published by Wiley in Mathematical Methods in the Applied Sciences
Open AccessWeak Solutions for a Class of Nonlocal Singular Problems Over the Nehari Manifold
In this paper, we consider a nonlocal model of dilatant non‐Newtonian fluid with a Dirichlet boundary condition. By using the Nehari manifold and fibering map methods, we obtain the existence of at least two weak solutions, with sign information. In detail, we construct two local minimizers of the energy functional associate to the main problem on proper Nehari submanifolds; in this way, we bypass the singularity to get boundedness below and coercivity of the functional. Then, we conclude that such minimizers correspond to weak solutions.
- Open Access
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
Inverse problem for nonstationary Oseen model with unilateral and frictional type boundary conditions
The goal of the research is to examine inverse problems to identify the divergence-free convection field and acting volume force in the nonstationary Oseen model of generalized Newtonian incompressible fluid. We provide a variational formulation of the flow model and establish existence result for weak solutions. The dependence of solution set on divergence-free convection field and volume force is examined too. Finally, we provide sufficient conditions under which the inverse problem is solvable.
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
Open AccessInverse problem for nonstationary Oseen model with unilateral and frictional type boundary conditions
The goal of the research is to examine inverse problems to identify the divergence-free convection field and acting volume force in the nonstationary Oseen model of generalized Newtonian incompressible fluid. We provide a variational formulation of the flow model and establish existence result for weak solutions. The dependence of solution set on divergence-free convection field and volume force is examined too. Finally, we provide sufficient conditions under which the inverse problem is solvable.
- 1 January 2026
- Published by AGH University Press in Opuscula Mathematica
- p. 101-119
Galerkin-type minimizers to a competing problem for \((\vec{p},\vec{q})\)-Laplacian with variable exponentsThis 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.- 1 January 2026
- Published by AGH University Press in Opuscula Mathematica
- p. 101-119
Galerkin-type minimizers to a competing problem for \((\vec{p},\vec{q})\)-Laplacian with variable exponentsThis 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.- Top Cited Papers
- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
- Vol. 22, 85-121
A class of double phase variable exponent energy functionals with different power growth and logarithmic perturbation
In this paper, we study a new kind of double phase variational exponents energy functional with log$ L $ -perturbed term, determined by the operator $ \begin{align} u\mapsto\Delta_{\mathcal {H}_{L}} u = \text{div} \left(\frac{\mathcal {H}'_{L}(x, |\nabla u|)}{|\nabla u|}\nabla u \right), \end{align} $ where $ \begin{align} \mathcal {H}_{L}(x, t) = [t^{p(x)}+\mu(x)t^{q(x)}]\log(e+\alpha t)\mbox{ for all }~~ x\in \Omega , \mbox{all} ~~ t\ge 0 , \mbox{some }~~ \alpha \geq 0 . \end{align} $ The features of the related Musielak-Orlicz Sobolev spaces are delivered. We further prove the density of smooth functions in such spaces in the case when the domain is bounded, or unbounded but with certain requirements. Finally, under very general assumptions on data, we show the existence and uniqueness results for weak solutions to a special class of perturbed Dirichlet double phase problems.- 1 January 2026
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
- Vol. 22, 85-121
Top Cited PapersA class of double phase variable exponent energy functionals with different power growth and logarithmic perturbation
In this paper, we study a new kind of double phase variational exponents energy functional with log$ L $ -perturbed term, determined by the operator $ \begin{align} u\mapsto\Delta_{\mathcal {H}_{L}} u = \text{div} \left(\frac{\mathcal {H}'_{L}(x, |\nabla u|)}{|\nabla u|}\nabla u \right), \end{align} $ where $ \begin{align} \mathcal {H}_{L}(x, t) = [t^{p(x)}+\mu(x)t^{q(x)}]\log(e+\alpha t)\mbox{ for all }~~ x\in \Omega , \mbox{all} ~~ t\ge 0 , \mbox{some }~~ \alpha \geq 0 . \end{align} $ The features of the related Musielak-Orlicz Sobolev spaces are delivered. We further prove the density of smooth functions in such spaces in the case when the domain is bounded, or unbounded but with certain requirements. Finally, under very general assumptions on data, we show the existence and uniqueness results for weak solutions to a special class of perturbed Dirichlet double phase problems. - 1 September 2025
- Published by Springer Nature
- p. 345-361
A Quasi-Linear Parabolic Inequality with Convection in Riemannian Manifolds
- 1 September 2025
- Published by Springer Nature
- p. 345-361
A Quasi-Linear Parabolic Inequality with Convection in Riemannian Manifolds
- Open Access
- 30 August 2025
- Published by MDPI AG in Fractal and Fractional
- Vol. 9 (9) , 574
Existence Results for Neumann Problem with Critical Sobolev–Hardy Exponent and Choquard-Type Nonlinearity
We consider a Neumann problem for the fractional Laplacian involving a nonlocal Choquard-type nonlinearity and Sobolev–Hardy exponent. Under suitable assumptions on the data and using the Nehari manifold method, we discuss the existence problem in several subcritical and critical cases.
- 30 August 2025
- Published by MDPI AG in Fractal and Fractional
- Vol. 9 (9) , 574
Open AccessExistence Results for Neumann Problem with Critical Sobolev–Hardy Exponent and Choquard-Type Nonlinearity
We consider a Neumann problem for the fractional Laplacian involving a nonlocal Choquard-type nonlinearity and Sobolev–Hardy exponent. Under suitable assumptions on the data and using the Nehari manifold method, we discuss the existence problem in several subcritical and critical cases.
- Open Access
- 23 July 2025
- Published by Springer Nature in Revista Matemática Complutense
- Vol. 39 (1) , 117-133
Nonlinear singular problems with an indefinite perturbation
We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which exhibits the competing effects of a parametric singular term and of a superlinear perturbation. Using variational methods together with truncation and comparison techniques, we show that for all small values of the parameter, the problem has at least two positive smooth solutions.
- 23 July 2025
- Published by Springer Nature in Revista Matemática Complutense
- Vol. 39 (1) , 117-133
Open AccessNonlinear singular problems with an indefinite perturbation
We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator and with a reaction which exhibits the competing effects of a parametric singular term and of a superlinear perturbation. Using variational methods together with truncation and comparison techniques, we show that for all small values of the parameter, the problem has at least two positive smooth solutions.